0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : vampire -m 90000 --mode casc -t %d %s 0.02/0.23 % Computer : n023.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 06:13:42 CDT 2018 0.02/0.23 % CPUTime : 0.02/0.24 Hi Geoff, go and have some cold beer while I am trying to solve this very hard problem! 0.02/0.24 % remaining time: 5999 next slice time: 4 0.02/0.27 lrs+1011_2_acc=on:add=off:afr=on:afp=40000:afq=2.0:amm=off:bd=off:bs=on:bsr=on:ccuc=small_ones:cond=on:er=filter:fsr=off:gs=on:gsem=on:irw=on:lcm=reverse:nwc=2:nicw=on:stl=30:sac=on:sp=occurrence:urr=on_2 on theBenchmark 0.52/0.77 % (13342)Time limit reached! 0.52/0.77 % ------------------------------ 0.52/0.77 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 0.52/0.77 % Termination reason: Time limit 0.52/0.77 % Termination phase: Saturation 0.52/0.77 0.52/0.77 % Memory used [KB]: 26225 0.52/0.77 % Time elapsed: 0.500 s 0.52/0.77 % ------------------------------ 0.52/0.77 % ------------------------------ 0.52/0.77 % remaining time: 5994 next slice time: 4 0.52/0.77 dis+1011_5:4_acc=model:afr=on:afp=10000:afq=1.4:amm=off:anc=none:bd=off:ccuc=small_ones:cond=fast:fde=unused:gs=on:nm=2:newcnf=on:nwc=1:nicw=on:sos=on:sac=on:sp=occurrence:updr=off_2 on theBenchmark 0.52/0.77 % Refutation not found, incomplete strategy 0.52/0.77 % ------------------------------ 0.52/0.77 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 0.52/0.77 % Termination reason: Refutation not found, incomplete strategy 0.52/0.77 0.52/0.77 % Memory used [KB]: 9850 0.52/0.77 % Time elapsed: 0.003 s 0.52/0.77 % ------------------------------ 0.52/0.77 % ------------------------------ 0.52/0.77 % remaining time: 5994 next slice time: 7 0.52/0.78 dis+11_5_av=off:bd=off:bs=unit_only:bsr=on:cond=on:lcm=reverse:nm=0:nwc=1.2_5 on theBenchmark 1.33/1.58 % (13344)Time limit reached! 1.33/1.58 % ------------------------------ 1.33/1.58 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.33/1.58 % Termination reason: Time limit 1.33/1.58 % Termination phase: Saturation 1.33/1.58 1.33/1.58 % Memory used [KB]: 22515 1.33/1.58 % Time elapsed: 0.800 s 1.33/1.58 % ------------------------------ 1.33/1.58 % ------------------------------ 1.33/1.58 % remaining time: 5986 next slice time: 4 1.33/1.58 dis+10_128_acc=on:add=off:afp=4000:afq=1.4:amm=off:bd=preordered:bce=on:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on_2 on theBenchmark 1.33/1.58 % Refutation not found, incomplete strategy 1.33/1.58 % ------------------------------ 1.33/1.58 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.33/1.58 % Termination reason: Refutation not found, incomplete strategy 1.33/1.58 1.33/1.58 % Memory used [KB]: 10106 1.33/1.58 % Time elapsed: 0.004 s 1.33/1.58 % ------------------------------ 1.33/1.58 % ------------------------------ 1.33/1.58 % remaining time: 5986 next slice time: 4 1.33/1.59 dis+10_1_add=off:afp=4000:afq=1.2:anc=none:br=off:cond=on:gs=on:irw=on:lcm=reverse:nwc=10:sd=10:ss=axioms:sos=theory:sac=on:sp=occurrence:urr=on_2 on theBenchmark 1.33/1.59 % Refutation not found, incomplete strategy 1.33/1.59 % ------------------------------ 1.33/1.59 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.33/1.59 % Termination reason: Refutation not found, incomplete strategy 1.33/1.59 1.33/1.59 % Memory used [KB]: 9722 1.33/1.59 % Time elapsed: 0.001 s 1.33/1.59 % ------------------------------ 1.33/1.59 % ------------------------------ 1.33/1.59 % remaining time: 5986 next slice time: 8 1.33/1.59 dis+10_3_add=large:afp=10000:afq=1.0:amm=sco:anc=none:gsp=input_only:gs=on:gsem=off:lcm=reverse:nwc=1:sos=on_6 on theBenchmark 1.33/1.59 % Refutation not found, incomplete strategy 1.33/1.59 % ------------------------------ 1.33/1.59 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 1.33/1.59 % Termination reason: Refutation not found, incomplete strategy 1.33/1.59 1.33/1.59 % Memory used [KB]: 9722 1.33/1.59 % Time elapsed: 0.002 s 1.33/1.59 % ------------------------------ 1.33/1.59 % ------------------------------ 1.33/1.59 % remaining time: 5986 next slice time: 7 1.33/1.59 dis+1011_4_av=off:cond=on:irw=on:lma=on:nm=2:nwc=1:sos=all:sp=occurrence_5 on theBenchmark 2.21/2.39 % (13348)Time limit reached! 2.21/2.39 % ------------------------------ 2.21/2.39 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 2.21/2.39 % Termination reason: Time limit 2.21/2.39 % Termination phase: Saturation 2.21/2.39 2.21/2.39 % Memory used [KB]: 14200 2.21/2.39 % Time elapsed: 0.800 s 2.21/2.39 % ------------------------------ 2.21/2.39 % ------------------------------ 2.21/2.39 % remaining time: 5978 next slice time: 52 2.21/2.39 dis+1010_3:1_av=off:gsp=input_only:nm=6:nwc=1:sos=all:sp=occurrence_49 on theBenchmark 7.54/7.69 % (13349)Time limit reached! 7.54/7.69 % ------------------------------ 7.54/7.69 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 7.54/7.69 % Termination reason: Time limit 7.54/7.69 % Termination phase: Saturation 7.54/7.69 7.54/7.69 % Memory used [KB]: 95179 7.54/7.69 % Time elapsed: 5.300 s 7.54/7.69 % ------------------------------ 7.54/7.69 % ------------------------------ 7.54/7.70 % remaining time: 5925 next slice time: 10 7.54/7.70 dis+10_3_add=off:afp=40000:afq=1.0:amm=sco:anc=none:er=filter:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1.3:sp=reverse_arity:updr=off_9 on theBenchmark 8.64/8.80 % (13350)Time limit reached! 8.64/8.80 % ------------------------------ 8.64/8.80 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 8.64/8.80 % Termination reason: Time limit 8.64/8.80 % Termination phase: Saturation 8.64/8.80 8.64/8.80 % Memory used [KB]: 56672 8.64/8.80 % Time elapsed: 1.100 s 8.64/8.80 % ------------------------------ 8.64/8.80 % ------------------------------ 8.64/8.81 % remaining time: 5914 next slice time: 131 8.64/8.81 ott+4_32_av=off:bsr=on:cond=on:er=known:fsr=off:gsp=input_only:gs=on:gsem=on:irw=on:lma=on:nm=4:nwc=1.2:sos=theory_124 on theBenchmark 19.90/20.03 % Refutation found. Thanks to Tanya! 19.90/20.03 % SZS status Theorem for theBenchmark 19.90/20.03 % SZS output start Proof for theBenchmark 19.90/20.08 fof(f3,axiom,( 19.90/20.08 substitution_of_equivalents <=> ! [X0,X1] : (is_a_theorem(equiv(X0,X1)) => X0 = X1)), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents)). 19.90/20.08 fof(f10,axiom,( 19.90/20.08 or_1 <=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1)). 19.90/20.08 fof(f27,axiom,( 19.90/20.08 op_or => ! [X0,X1] : not(and(not(X0),not(X1))) = or(X0,X1)), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or)). 19.90/20.08 fof(f29,axiom,( 19.90/20.08 op_implies_and => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and)). 19.90/20.08 fof(f31,axiom,( 19.90/20.08 op_equiv => ! [X0,X1] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1)), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv)). 19.90/20.08 fof(f33,axiom,( 19.90/20.08 axiom_m5 <=> ! [X0,X1,X5] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X5)),strict_implies(X0,X5)))), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5)). 19.90/20.08 fof(f37,axiom,( 19.90/20.08 ! [X0,X1] : (is_a_theorem(strict_equiv(X0,X1)) => X0 = X1) <=> substitution_strict_equiv), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv)). 19.90/20.08 fof(f39,axiom,( 19.90/20.08 ! [X0,X1,X5] : is_a_theorem(strict_implies(and(and(X0,X1),X5),and(X0,and(X1,X5)))) <=> axiom_m3), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m3)). 19.90/20.08 fof(f42,axiom,( 19.90/20.08 ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(strict_implies(X0,X1))) => is_a_theorem(X1)) <=> modus_ponens_strict_implies), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies)). 19.90/20.08 fof(f45,axiom,( 19.90/20.08 ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) <=> axiom_m1), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1)). 19.90/20.08 fof(f46,axiom,( 19.90/20.08 axiom_m4 <=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4)). 19.90/20.08 fof(f53,axiom,( 19.90/20.08 adjunction <=> ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(X1)) => is_a_theorem(and(X0,X1)))), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction)). 19.90/20.08 fof(f54,axiom,( 19.90/20.08 ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) <=> axiom_m2), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2)). 19.90/20.08 fof(f55,axiom,( 19.90/20.08 op_strict_equiv => ! [X0,X1] : and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1)), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv)). 19.90/20.08 fof(f57,axiom,( 19.90/20.08 op_strict_implies => ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies)). 19.90/20.08 fof(f59,axiom,( 19.90/20.08 axiom_m1), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1)). 19.90/20.08 fof(f60,axiom,( 19.90/20.08 substitution_strict_equiv), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv)). 19.90/20.08 fof(f61,axiom,( 19.90/20.08 op_strict_implies), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies)). 19.90/20.08 fof(f62,axiom,( 19.90/20.08 adjunction), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_adjunction)). 19.90/20.08 fof(f63,axiom,( 19.90/20.08 axiom_m3), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m3)). 19.90/20.08 fof(f64,axiom,( 19.90/20.08 axiom_m5), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m5)). 19.90/20.08 fof(f65,axiom,( 19.90/20.08 axiom_m4), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4)). 19.90/20.08 fof(f66,axiom,( 19.90/20.08 op_strict_equiv), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv)). 19.90/20.08 fof(f67,axiom,( 19.90/20.08 modus_ponens_strict_implies), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies)). 19.90/20.08 fof(f68,axiom,( 19.90/20.08 axiom_m2), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2)). 19.90/20.08 fof(f73,axiom,( 19.90/20.08 op_equiv), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv)). 19.90/20.08 fof(f74,axiom,( 19.90/20.08 substitution_of_equivalents), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents)). 19.90/20.08 fof(f75,axiom,( 19.90/20.08 op_or), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or)). 19.90/20.08 fof(f76,conjecture,( 19.90/20.08 or_1), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1)). 19.90/20.08 fof(f77,negated_conjecture,( 19.90/20.08 ~or_1), 19.90/20.08 inference(negated_conjecture,[],[f76])). 19.90/20.08 fof(f78,axiom,( 19.90/20.08 op_implies_and), 19.90/20.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and)). 19.90/20.08 fof(f79,plain,( 19.90/20.08 ~or_1), 19.90/20.08 inference(flattening,[],[f77])). 19.90/20.08 fof(f90,plain,( 19.90/20.08 axiom_m5 <=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))), 19.90/20.08 inference(rectify,[],[f33])). 19.90/20.08 fof(f98,plain,( 19.90/20.08 ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) <=> axiom_m3), 19.90/20.08 inference(rectify,[],[f39])). 19.90/20.08 fof(f99,plain,( 19.90/20.08 axiom_m2 => ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f54])). 19.90/20.08 fof(f100,plain,( 19.90/20.08 adjunction => ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(X1)) => is_a_theorem(and(X0,X1)))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f53])). 19.90/20.08 fof(f101,plain,( 19.90/20.08 axiom_m4 => ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f46])). 19.90/20.08 fof(f102,plain,( 19.90/20.08 axiom_m1 => ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f45])). 19.90/20.08 fof(f103,plain,( 19.90/20.08 modus_ponens_strict_implies => ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(strict_implies(X0,X1))) => is_a_theorem(X1))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f42])). 19.90/20.08 fof(f104,plain,( 19.90/20.08 axiom_m3 => ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f98])). 19.90/20.08 fof(f105,plain,( 19.90/20.08 substitution_strict_equiv => ! [X0,X1] : (is_a_theorem(strict_equiv(X0,X1)) => X0 = X1)), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f37])). 19.90/20.08 fof(f106,plain,( 19.90/20.08 axiom_m5 => ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f90])). 19.90/20.08 fof(f107,plain,( 19.90/20.08 ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) => or_1), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f10])). 19.90/20.08 fof(f108,plain,( 19.90/20.08 substitution_of_equivalents => ! [X0,X1] : (is_a_theorem(equiv(X0,X1)) => X0 = X1)), 19.90/20.08 inference(unused_predicate_definition_removal,[],[f3])). 19.90/20.08 fof(f114,plain,( 19.90/20.08 ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) | ~op_strict_implies), 19.90/20.08 inference(ennf_transformation,[],[f57])). 19.90/20.08 fof(f115,plain,( 19.90/20.08 ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) | ~op_implies_and), 19.90/20.08 inference(ennf_transformation,[],[f29])). 19.90/20.08 fof(f116,plain,( 19.90/20.08 ! [X0,X1] : and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) | ~op_strict_equiv), 19.90/20.08 inference(ennf_transformation,[],[f55])). 19.90/20.08 fof(f117,plain,( 19.90/20.08 ! [X0,X1] : not(and(not(X0),not(X1))) = or(X0,X1) | ~op_or), 19.90/20.08 inference(ennf_transformation,[],[f27])). 19.90/20.08 fof(f118,plain,( 19.90/20.08 ! [X0,X1] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) | ~op_equiv), 19.90/20.08 inference(ennf_transformation,[],[f31])). 19.90/20.08 fof(f119,plain,( 19.90/20.08 or_1 | ? [X0,X1] : ~is_a_theorem(implies(X0,or(X0,X1)))), 19.90/20.08 inference(ennf_transformation,[],[f107])). 19.90/20.08 fof(f120,plain,( 19.90/20.08 ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) | ~axiom_m4), 19.90/20.08 inference(ennf_transformation,[],[f101])). 19.90/20.08 fof(f121,plain,( 19.90/20.08 ! [X0,X1] : (X0 = X1 | ~is_a_theorem(equiv(X0,X1))) | ~substitution_of_equivalents), 19.90/20.08 inference(ennf_transformation,[],[f108])). 19.90/20.08 fof(f122,plain,( 19.90/20.08 ! [X0,X1] : (is_a_theorem(and(X0,X1)) | (~is_a_theorem(X0) | ~is_a_theorem(X1))) | ~adjunction), 19.90/20.08 inference(ennf_transformation,[],[f100])). 19.90/20.08 fof(f123,plain,( 19.90/20.08 ! [X0,X1] : (is_a_theorem(and(X0,X1)) | ~is_a_theorem(X0) | ~is_a_theorem(X1)) | ~adjunction), 19.90/20.08 inference(flattening,[],[f122])). 19.90/20.08 fof(f124,plain,( 19.90/20.08 ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) | ~axiom_m5), 19.90/20.08 inference(ennf_transformation,[],[f106])). 19.90/20.08 fof(f125,plain,( 19.90/20.08 ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) | ~axiom_m2), 19.90/20.08 inference(ennf_transformation,[],[f99])). 19.90/20.08 fof(f126,plain,( 19.90/20.08 ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) | ~axiom_m1), 19.90/20.08 inference(ennf_transformation,[],[f102])). 19.90/20.08 fof(f127,plain,( 19.90/20.08 ! [X0,X1] : (X0 = X1 | ~is_a_theorem(strict_equiv(X0,X1))) | ~substitution_strict_equiv), 19.90/20.08 inference(ennf_transformation,[],[f105])). 19.90/20.08 fof(f128,plain,( 19.90/20.08 ! [X0,X1] : (is_a_theorem(X1) | (~is_a_theorem(X0) | ~is_a_theorem(strict_implies(X0,X1)))) | ~modus_ponens_strict_implies), 19.90/20.08 inference(ennf_transformation,[],[f103])). 19.90/20.08 fof(f129,plain,( 19.90/20.08 ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(X0) | ~is_a_theorem(strict_implies(X0,X1))) | ~modus_ponens_strict_implies), 19.90/20.08 inference(flattening,[],[f128])). 19.90/20.08 fof(f130,plain,( 19.90/20.08 ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) | ~axiom_m3), 19.90/20.08 inference(ennf_transformation,[],[f104])). 19.90/20.08 fof(f131,plain,( 19.90/20.08 ? [X0,X1] : ~is_a_theorem(implies(X0,or(X0,X1))) => ~is_a_theorem(implies(sK0,or(sK0,sK1)))), 19.90/20.08 introduced(choice_axiom,[])). 19.90/20.08 fof(f132,plain,( 19.90/20.08 or_1 | ~is_a_theorem(implies(sK0,or(sK0,sK1)))), 19.90/20.08 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f119,f131])). 19.90/20.08 fof(f133,plain,( 19.90/20.08 ~or_1), 19.90/20.08 inference(cnf_transformation,[],[f79])). 19.90/20.08 fof(f134,plain,( 19.90/20.08 modus_ponens_strict_implies), 19.90/20.08 inference(cnf_transformation,[],[f67])). 19.90/20.08 fof(f135,plain,( 19.90/20.08 axiom_m1), 19.90/20.08 inference(cnf_transformation,[],[f59])). 19.90/20.08 fof(f136,plain,( 19.90/20.08 substitution_strict_equiv), 19.90/20.08 inference(cnf_transformation,[],[f60])). 19.90/20.08 fof(f137,plain,( 19.90/20.08 axiom_m4), 19.90/20.08 inference(cnf_transformation,[],[f65])). 19.90/20.08 fof(f138,plain,( 19.90/20.08 substitution_of_equivalents), 19.90/20.08 inference(cnf_transformation,[],[f74])). 19.90/20.08 fof(f139,plain,( 19.90/20.08 adjunction), 19.90/20.08 inference(cnf_transformation,[],[f62])). 19.90/20.08 fof(f140,plain,( 19.90/20.08 axiom_m3), 19.90/20.08 inference(cnf_transformation,[],[f63])). 19.90/20.08 fof(f141,plain,( 19.90/20.08 axiom_m5), 19.90/20.08 inference(cnf_transformation,[],[f64])). 19.90/20.08 fof(f142,plain,( 19.90/20.08 axiom_m2), 19.90/20.08 inference(cnf_transformation,[],[f68])). 19.90/20.08 fof(f143,plain,( 19.90/20.08 op_implies_and), 19.90/20.08 inference(cnf_transformation,[],[f78])). 19.90/20.08 fof(f144,plain,( 19.90/20.08 op_strict_equiv), 19.90/20.08 inference(cnf_transformation,[],[f66])). 19.90/20.08 fof(f145,plain,( 19.90/20.08 op_strict_implies), 19.90/20.08 inference(cnf_transformation,[],[f61])). 19.90/20.08 fof(f147,plain,( 19.90/20.08 op_or), 19.90/20.08 inference(cnf_transformation,[],[f75])). 19.90/20.08 fof(f148,plain,( 19.90/20.08 op_equiv), 19.90/20.08 inference(cnf_transformation,[],[f73])). 19.90/20.08 fof(f152,plain,( 19.90/20.08 ( ! [X0,X1] : (strict_implies(X0,X1) = necessarily(implies(X0,X1)) | ~op_strict_implies) )), 19.90/20.08 inference(cnf_transformation,[],[f114])). 19.90/20.08 fof(f153,plain,( 19.90/20.08 ( ! [X0,X1] : (implies(X0,X1) = not(and(X0,not(X1))) | ~op_implies_and) )), 19.90/20.08 inference(cnf_transformation,[],[f115])). 19.90/20.08 fof(f154,plain,( 19.90/20.08 ( ! [X0,X1] : (and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) | ~op_strict_equiv) )), 19.90/20.08 inference(cnf_transformation,[],[f116])). 19.90/20.08 fof(f155,plain,( 19.90/20.08 ( ! [X0,X1] : (not(and(not(X0),not(X1))) = or(X0,X1) | ~op_or) )), 19.90/20.08 inference(cnf_transformation,[],[f117])). 19.90/20.08 fof(f156,plain,( 19.90/20.08 ( ! [X0,X1] : (and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) | ~op_equiv) )), 19.90/20.08 inference(cnf_transformation,[],[f118])). 19.90/20.08 fof(f157,plain,( 19.90/20.08 or_1 | ~is_a_theorem(implies(sK0,or(sK0,sK1)))), 19.90/20.08 inference(cnf_transformation,[],[f132])). 19.90/20.08 fof(f158,plain,( 19.90/20.08 ( ! [X0] : (is_a_theorem(strict_implies(X0,and(X0,X0))) | ~axiom_m4) )), 19.90/20.08 inference(cnf_transformation,[],[f120])). 19.90/20.08 fof(f159,plain,( 19.90/20.08 ( ! [X0,X1] : (X0 = X1 | ~is_a_theorem(equiv(X0,X1)) | ~substitution_of_equivalents) )), 19.90/20.08 inference(cnf_transformation,[],[f121])). 19.90/20.08 fof(f160,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(and(X0,X1)) | ~is_a_theorem(X0) | ~is_a_theorem(X1) | ~adjunction) )), 19.90/20.08 inference(cnf_transformation,[],[f123])). 19.90/20.08 fof(f161,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) | ~axiom_m5) )), 19.90/20.08 inference(cnf_transformation,[],[f124])). 19.90/20.08 fof(f162,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),X0)) | ~axiom_m2) )), 19.90/20.08 inference(cnf_transformation,[],[f125])). 19.90/20.08 fof(f163,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) | ~axiom_m1) )), 19.90/20.08 inference(cnf_transformation,[],[f126])). 19.90/20.08 fof(f164,plain,( 19.90/20.08 ( ! [X0,X1] : (X0 = X1 | ~is_a_theorem(strict_equiv(X0,X1)) | ~substitution_strict_equiv) )), 19.90/20.08 inference(cnf_transformation,[],[f127])). 19.90/20.08 fof(f165,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(X0) | ~is_a_theorem(strict_implies(X0,X1)) | ~modus_ponens_strict_implies) )), 19.90/20.08 inference(cnf_transformation,[],[f129])). 19.90/20.08 fof(f166,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) | ~axiom_m3) )), 19.90/20.08 inference(cnf_transformation,[],[f130])). 19.90/20.08 fof(f168,plain,( 19.90/20.08 ( ! [X0,X1] : (strict_implies(X0,X1) = necessarily(implies(X0,X1))) )), 19.90/20.08 inference(global_subsumption,[],[f145,f152])). 19.90/20.08 fof(f169,plain,( 19.90/20.08 ( ! [X0,X1] : (implies(X0,X1) = not(and(X0,not(X1)))) )), 19.90/20.08 inference(global_subsumption,[],[f143,f153])). 19.90/20.08 fof(f170,plain,( 19.90/20.08 ( ! [X0,X1] : (and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1)) )), 19.90/20.08 inference(global_subsumption,[],[f144,f154])). 19.90/20.08 fof(f171,plain,( 19.90/20.08 ( ! [X0,X1] : (implies(not(X0),X1) = or(X0,X1) | ~op_or) )), 19.90/20.08 inference(forward_demodulation,[],[f155,f169])). 19.90/20.08 fof(f172,plain,( 19.90/20.08 ( ! [X0,X1] : (implies(not(X0),X1) = or(X0,X1)) )), 19.90/20.08 inference(global_subsumption,[],[f147,f171])). 19.90/20.08 fof(f173,plain,( 19.90/20.08 ( ! [X0,X1] : (and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1)) )), 19.90/20.08 inference(global_subsumption,[],[f148,f156])). 19.90/20.08 fof(f174,plain,( 19.90/20.08 ~is_a_theorem(implies(sK0,or(sK0,sK1)))), 19.90/20.08 inference(global_subsumption,[],[f133,f157])). 19.90/20.08 fof(f175,plain,( 19.90/20.08 ( ! [X0] : (is_a_theorem(strict_implies(X0,and(X0,X0)))) )), 19.90/20.08 inference(global_subsumption,[],[f137,f158])). 19.90/20.08 fof(f176,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(equiv(X0,X1)) | X0 = X1) )), 19.90/20.08 inference(global_subsumption,[],[f138,f159])). 19.90/20.08 fof(f177,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(and(X0,X1)) | ~is_a_theorem(X0) | ~is_a_theorem(X1)) )), 19.90/20.08 inference(global_subsumption,[],[f139,f160])). 19.90/20.08 fof(f178,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))) )), 19.90/20.08 inference(global_subsumption,[],[f141,f161])). 19.90/20.08 fof(f179,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),X0))) )), 19.90/20.08 inference(global_subsumption,[],[f142,f162])). 19.90/20.08 fof(f180,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))) )), 19.90/20.08 inference(global_subsumption,[],[f135,f163])). 19.90/20.08 fof(f181,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(strict_equiv(X0,X1)) | X0 = X1) )), 19.90/20.08 inference(global_subsumption,[],[f136,f164])). 19.90/20.08 fof(f182,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(strict_implies(X0,X1)) | ~is_a_theorem(X0) | is_a_theorem(X1)) )), 19.90/20.08 inference(global_subsumption,[],[f134,f165])). 19.90/20.08 fof(f183,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))) )), 19.90/20.08 inference(global_subsumption,[],[f140,f166])). 19.90/20.08 fof(f186,plain,( 19.90/20.08 ( ! [X0,X1] : (strict_implies(not(X0),X1) = necessarily(or(X0,X1))) )), 19.90/20.08 inference(superposition,[],[f168,f172])). 19.90/20.08 fof(f195,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3)))) )), 19.90/20.08 inference(superposition,[],[f169,f169])). 19.90/20.08 fof(f196,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (implies(implies(X0,X1),X2) = or(and(X0,not(X1)),X2)) )), 19.90/20.08 inference(superposition,[],[f172,f169])). 19.90/20.08 fof(f206,plain,( 19.90/20.08 ( ! [X0] : (is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))) )), 19.90/20.08 inference(superposition,[],[f175,f186])). 19.90/20.08 fof(f224,plain,( 19.90/20.08 ( ! [X10,X11] : (is_a_theorem(strict_equiv(X10,X11)) | ~is_a_theorem(strict_implies(X10,X11)) | ~is_a_theorem(strict_implies(X11,X10))) )), 19.90/20.08 inference(superposition,[],[f177,f170])). 19.90/20.08 fof(f279,plain,( 19.90/20.08 ( ! [X10,X11] : (is_a_theorem(equiv(X10,X11)) | ~is_a_theorem(implies(X10,X11)) | ~is_a_theorem(implies(X11,X10))) )), 19.90/20.08 inference(superposition,[],[f177,f173])). 19.90/20.08 fof(f336,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (~is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2))) | is_a_theorem(strict_implies(X0,X2))) )), 19.90/20.08 inference(resolution,[],[f178,f182])). 19.90/20.08 fof(f391,plain,( 19.90/20.08 ( ! [X6,X7] : (~is_a_theorem(strict_implies(X7,X6)) | ~is_a_theorem(strict_implies(X6,X7)) | X6 = X7) )), 19.90/20.08 inference(resolution,[],[f224,f181])). 19.90/20.08 fof(f396,plain,( 19.90/20.08 ( ! [X0] : (~is_a_theorem(strict_implies(and(X0,X0),X0)) | and(X0,X0) = X0) )), 19.90/20.08 inference(resolution,[],[f391,f175])). 19.90/20.08 fof(f397,plain,( 19.90/20.08 ( ! [X2,X1] : (~is_a_theorem(strict_implies(X1,and(X1,X2))) | and(X1,X2) = X1) )), 19.90/20.08 inference(resolution,[],[f391,f179])). 19.90/20.08 fof(f398,plain,( 19.90/20.08 ( ! [X4,X3] : (~is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))) | and(X3,X4) = and(X4,X3)) )), 19.90/20.08 inference(resolution,[],[f391,f180])). 19.90/20.08 fof(f400,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (~is_a_theorem(strict_implies(and(X8,and(X9,X10)),and(and(X8,X9),X10))) | and(X8,and(X9,X10)) = and(and(X8,X9),X10)) )), 19.90/20.08 inference(resolution,[],[f391,f183])). 19.90/20.08 fof(f413,plain,( 19.90/20.08 ( ! [X4,X3] : (and(X3,X4) = and(X4,X3)) )), 19.90/20.08 inference(global_subsumption,[],[f180,f398])). 19.90/20.08 fof(f421,plain,( 19.90/20.08 ( ! [X4,X5] : (~is_a_theorem(implies(X5,X4)) | ~is_a_theorem(implies(X4,X5)) | X4 = X5) )), 19.90/20.08 inference(resolution,[],[f279,f176])). 19.90/20.08 fof(f425,plain,( 19.90/20.08 ( ! [X2,X3] : (and(implies(X3,X2),implies(X2,X3)) = equiv(X2,X3)) )), 19.90/20.08 inference(superposition,[],[f413,f173])). 19.90/20.08 fof(f429,plain,( 19.90/20.08 ( ! [X4,X5] : (is_a_theorem(strict_implies(and(X5,X4),X4))) )), 19.90/20.08 inference(superposition,[],[f179,f413])). 19.90/20.08 fof(f432,plain,( 19.90/20.08 ( ! [X12,X10,X11] : (is_a_theorem(strict_implies(and(and(X11,X10),X12),and(X10,and(X11,X12))))) )), 19.90/20.08 inference(superposition,[],[f183,f413])). 19.90/20.08 fof(f433,plain,( 19.90/20.08 ( ! [X14,X15,X13] : (is_a_theorem(strict_implies(and(and(X15,X13),X14),and(X15,and(X14,X13))))) )), 19.90/20.08 inference(superposition,[],[f183,f413])). 19.90/20.08 fof(f436,plain,( 19.90/20.08 ( ! [X21,X22,X20] : (is_a_theorem(strict_implies(and(and(X20,X21),X22),and(and(X21,X22),X20)))) )), 19.90/20.08 inference(superposition,[],[f183,f413])). 19.90/20.08 fof(f439,plain,( 19.90/20.08 ( ! [X28,X29] : (implies(X28,X29) = not(and(not(X29),X28))) )), 19.90/20.08 inference(superposition,[],[f169,f413])). 19.90/20.08 fof(f440,plain,( 19.90/20.08 ( ! [X30,X31,X32] : (is_a_theorem(strict_implies(and(X32,and(X30,X31)),and(X30,and(X31,X32))))) )), 19.90/20.08 inference(superposition,[],[f183,f413])). 19.90/20.08 fof(f460,plain,( 19.90/20.08 ( ! [X0] : (and(X0,X0) = X0) )), 19.90/20.08 inference(subsumption_resolution,[],[f396,f429])). 19.90/20.08 fof(f462,plain,( 19.90/20.08 ( ! [X0] : (is_a_theorem(strict_implies(X0,X0))) )), 19.90/20.08 inference(backward_demodulation,[],[f460,f175])). 19.90/20.08 fof(f463,plain,( 19.90/20.08 ( ! [X0] : (is_a_theorem(necessarily(or(X0,not(X0))))) )), 19.90/20.08 inference(backward_demodulation,[],[f460,f206])). 19.90/20.08 fof(f481,plain,( 19.90/20.08 ( ! [X4,X5] : (is_a_theorem(strict_implies(and(X4,X5),and(X4,and(X4,X5))))) )), 19.90/20.08 inference(superposition,[],[f183,f460])). 19.90/20.08 fof(f488,plain,( 19.90/20.08 ( ! [X17] : (implies(not(X17),X17) = not(not(X17))) )), 19.90/20.08 inference(superposition,[],[f169,f460])). 19.90/20.08 fof(f525,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(strict_implies(X0,and(X1,X0))) | and(X1,X0) = X0) )), 19.90/20.08 inference(resolution,[],[f429,f391])). 19.90/20.08 fof(f613,plain,( 19.90/20.08 ( ! [X2,X1] : (implies(implies(X1,X2),and(X1,not(X2))) = not(implies(X1,X2))) )), 19.90/20.08 inference(superposition,[],[f488,f169])). 19.90/20.08 fof(f614,plain,( 19.90/20.08 ( ! [X0] : (not(not(X0)) = or(X0,X0)) )), 19.90/20.08 inference(superposition,[],[f488,f172])). 19.90/20.08 fof(f618,plain,( 19.90/20.08 ( ! [X2] : (and(implies(X2,not(X2)),not(not(X2))) = equiv(X2,not(X2))) )), 19.90/20.08 inference(superposition,[],[f173,f488])). 19.90/20.08 fof(f672,plain,( 19.90/20.08 ( ! [X6,X7,X5] : (implies(X7,and(not(X5),X6)) = not(and(implies(X6,X5),X7))) )), 19.90/20.08 inference(superposition,[],[f439,f439])). 19.90/20.08 fof(f676,plain,( 19.90/20.08 ( ! [X2,X3] : (implies(not(X2),X3) = implies(not(X3),X2)) )), 19.90/20.08 inference(superposition,[],[f439,f169])). 19.90/20.08 fof(f696,plain,( 19.90/20.08 ( ! [X2,X3] : (implies(not(X2),X3) = or(X3,X2)) )), 19.90/20.08 inference(forward_demodulation,[],[f676,f172])). 19.90/20.08 fof(f720,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (implies(implies(X2,X3),X4) = or(X4,and(X2,not(X3)))) )), 19.90/20.08 inference(superposition,[],[f696,f169])). 19.90/20.08 fof(f721,plain,( 19.90/20.08 ( ! [X6,X7,X5] : (implies(implies(X6,X5),X7) = or(X7,and(not(X5),X6))) )), 19.90/20.08 inference(superposition,[],[f696,f439])). 19.90/20.08 fof(f731,plain,( 19.90/20.08 ( ! [X12,X11] : (strict_implies(not(X11),X12) = necessarily(or(X12,X11))) )), 19.90/20.08 inference(superposition,[],[f168,f696])). 19.90/20.08 fof(f847,plain,( 19.90/20.08 ( ! [X2,X3] : (necessarily(or(X2,X3)) = necessarily(or(X3,X2))) )), 19.90/20.08 inference(superposition,[],[f731,f186])). 19.90/20.08 fof(f915,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (~is_a_theorem(strict_implies(X2,X1)) | ~is_a_theorem(strict_implies(X0,X2)) | is_a_theorem(strict_implies(X0,X1))) )), 19.90/20.08 inference(resolution,[],[f336,f177])). 19.90/20.08 fof(f982,plain,( 19.90/20.08 ( ! [X4,X5] : (is_a_theorem(strict_implies(and(X5,X4),and(X4,and(X5,X4))))) )), 19.90/20.08 inference(superposition,[],[f481,f413])). 19.90/20.08 fof(f1266,plain,( 19.90/20.08 ( ! [X4,X5] : (~is_a_theorem(strict_implies(X4,and(X5,X4))) | and(X4,X5) = X4) )), 19.90/20.08 inference(superposition,[],[f397,f413])). 19.90/20.08 fof(f1395,plain,( 19.90/20.08 ( ! [X0,X1] : (and(X0,X1) = and(and(X0,X1),X1)) )), 19.90/20.08 inference(resolution,[],[f1266,f982])). 19.90/20.08 fof(f1396,plain,( 19.90/20.08 ( ! [X2,X3] : (and(X2,X3) = and(and(X2,X3),X2)) )), 19.90/20.08 inference(resolution,[],[f1266,f481])). 19.90/20.08 fof(f1419,plain,( 19.90/20.08 ( ! [X8,X7] : (and(equiv(X8,X7),implies(X7,X8)) = equiv(X8,X7)) )), 19.90/20.08 inference(superposition,[],[f1396,f425])). 19.90/20.08 fof(f1451,plain,( 19.90/20.08 ( ! [X57,X56] : (implies(and(not(X56),X57),X56) = not(and(not(X56),X57))) )), 19.90/20.08 inference(superposition,[],[f169,f1396])). 19.90/20.08 fof(f1481,plain,( 19.90/20.08 ( ! [X57,X56] : (implies(X57,X56) = implies(and(not(X56),X57),X56)) )), 19.90/20.08 inference(forward_demodulation,[],[f1451,f439])). 19.90/20.08 fof(f1491,plain,( 19.90/20.08 ( ! [X4,X3] : (and(X3,X4) = and(X4,and(X3,X4))) )), 19.90/20.08 inference(superposition,[],[f1395,f413])). 19.90/20.08 fof(f1633,plain,( 19.90/20.08 ( ! [X0,X1] : (strict_implies(and(not(X0),X1),X0) = necessarily(implies(X1,X0))) )), 19.90/20.08 inference(superposition,[],[f168,f1481])). 19.90/20.08 fof(f1648,plain,( 19.90/20.08 ( ! [X0,X1] : (strict_implies(X1,X0) = strict_implies(and(not(X0),X1),X0)) )), 19.90/20.08 inference(forward_demodulation,[],[f1633,f168])). 19.90/20.08 fof(f1783,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(necessarily(or(and(X1,not(X0)),X0))) | and(X1,not(X0)) = not(X0)) )), 19.90/20.08 inference(superposition,[],[f525,f731])). 19.90/20.08 fof(f1791,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(necessarily(or(X0,and(X1,not(X0))))) | and(X1,not(X0)) = not(X0)) )), 19.90/20.08 inference(forward_demodulation,[],[f1783,f847])). 19.90/20.08 fof(f1792,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(necessarily(implies(implies(X1,X0),X0))) | and(X1,not(X0)) = not(X0)) )), 19.90/20.08 inference(forward_demodulation,[],[f1791,f720])). 19.90/20.08 fof(f1793,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(strict_implies(implies(X1,X0),X0)) | and(X1,not(X0)) = not(X0)) )), 19.90/20.08 inference(forward_demodulation,[],[f1792,f168])). 19.90/20.08 fof(f2016,plain,( 19.90/20.08 ( ! [X12] : (and(equiv(X12,not(X12)),not(not(X12))) = equiv(X12,not(X12))) )), 19.90/20.08 inference(superposition,[],[f1419,f488])). 19.90/20.08 fof(f2962,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (strict_implies(X0,and(X1,not(X2))) = necessarily(not(and(X0,implies(X1,X2))))) )), 19.90/20.08 inference(superposition,[],[f168,f195])). 19.90/20.08 fof(f3075,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (~is_a_theorem(strict_implies(X2,and(X3,X4))) | is_a_theorem(strict_implies(X2,X3))) )), 19.90/20.08 inference(resolution,[],[f915,f179])). 19.90/20.08 fof(f3076,plain,( 19.90/20.08 ( ! [X6,X7,X5] : (~is_a_theorem(strict_implies(X5,and(X6,X7))) | is_a_theorem(strict_implies(X5,and(X7,X6)))) )), 19.90/20.08 inference(resolution,[],[f915,f180])). 19.90/20.08 fof(f3077,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (~is_a_theorem(strict_implies(X8,and(X9,X10))) | is_a_theorem(strict_implies(X8,X10))) )), 19.90/20.08 inference(resolution,[],[f915,f429])). 19.90/20.08 fof(f3116,plain,( 19.90/20.08 ( ! [X8,X7,X9] : (is_a_theorem(strict_implies(and(X7,and(X8,X9)),X8))) )), 19.90/20.08 inference(resolution,[],[f3075,f429])). 19.90/20.08 fof(f3137,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (~is_a_theorem(necessarily(or(and(X1,X2),X0))) | is_a_theorem(strict_implies(not(X0),X1))) )), 19.90/20.08 inference(superposition,[],[f3075,f731])). 19.90/20.08 fof(f3142,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (~is_a_theorem(necessarily(or(and(X1,X2),X0))) | is_a_theorem(necessarily(or(X0,X1)))) )), 19.90/20.08 inference(forward_demodulation,[],[f3137,f186])). 19.90/20.08 fof(f6921,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X0,X2),X1)))) )), 19.90/20.08 inference(resolution,[],[f432,f3076])). 19.90/20.08 fof(f6926,plain,( 19.90/20.08 ( ! [X17,X18,X16] : (~is_a_theorem(strict_implies(and(X16,and(X17,X18)),and(and(X17,X16),X18))) | and(X16,and(X17,X18)) = and(and(X17,X16),X18)) )), 19.90/20.08 inference(resolution,[],[f432,f391])). 19.90/20.08 fof(f7025,plain,( 19.90/20.08 ( ! [X6,X4,X5] : (is_a_theorem(strict_implies(and(X6,and(X4,X5)),and(X4,and(X6,X5))))) )), 19.90/20.08 inference(superposition,[],[f433,f413])). 19.90/20.08 fof(f7312,plain,( 19.90/20.08 ( ! [X17,X18,X16] : (~is_a_theorem(strict_implies(and(X16,and(X17,X18)),and(X18,and(X16,X17)))) | and(X16,and(X17,X18)) = and(X18,and(X16,X17))) )), 19.90/20.08 inference(resolution,[],[f440,f391])). 19.90/20.08 fof(f8419,plain,( 19.90/20.08 ( ! [X21,X19,X20] : (~is_a_theorem(strict_implies(and(and(X19,X20),X21),and(and(X19,X21),X20))) | and(and(X19,X20),X21) = and(and(X19,X21),X20)) )), 19.90/20.08 inference(resolution,[],[f6921,f391])). 19.90/20.08 fof(f8444,plain,( 19.90/20.08 ( ! [X6,X4,X5] : (is_a_theorem(strict_implies(and(X6,and(X4,X5)),and(and(X4,X6),X5)))) )), 19.90/20.08 inference(superposition,[],[f6921,f413])). 19.90/20.08 fof(f8477,plain,( 19.90/20.08 ( ! [X21,X19,X20] : (and(and(X19,X20),X21) = and(and(X19,X21),X20)) )), 19.90/20.08 inference(global_subsumption,[],[f6921,f8419])). 19.90/20.08 fof(f8496,plain,( 19.90/20.08 ( ! [X17,X18,X16] : (and(X16,and(X17,X18)) = and(and(X17,X16),X18)) )), 19.90/20.08 inference(subsumption_resolution,[],[f6926,f8444])). 19.90/20.08 fof(f8499,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (~is_a_theorem(strict_implies(and(X8,and(X9,X10)),and(X9,and(X8,X10)))) | and(X8,and(X9,X10)) = and(and(X8,X9),X10)) )), 19.90/20.08 inference(backward_demodulation,[],[f8496,f400])). 19.90/20.08 fof(f8502,plain,( 19.90/20.08 ( ! [X21,X22,X20] : (is_a_theorem(strict_implies(and(and(X20,X21),X22),and(X22,and(X21,X20))))) )), 19.90/20.08 inference(backward_demodulation,[],[f8496,f436])). 19.90/20.08 fof(f8726,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (and(X8,and(X9,X10)) = and(X9,and(X8,X10)) | ~is_a_theorem(strict_implies(and(X8,and(X9,X10)),and(X9,and(X8,X10))))) )), 19.90/20.08 inference(forward_demodulation,[],[f8499,f8496])). 19.90/20.08 fof(f8727,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (and(X8,and(X9,X10)) = and(X9,and(X8,X10))) )), 19.90/20.08 inference(global_subsumption,[],[f7025,f8726])). 19.90/20.08 fof(f8774,plain,( 19.90/20.08 ( ! [X21,X22,X20] : (is_a_theorem(strict_implies(and(X21,and(X20,X22)),and(X22,and(X21,X20))))) )), 19.90/20.08 inference(forward_demodulation,[],[f8502,f8496])). 19.90/20.08 fof(f8775,plain,( 19.90/20.08 ( ! [X17,X18,X16] : (and(X16,and(X17,X18)) = and(X18,and(X16,X17))) )), 19.90/20.08 inference(subsumption_resolution,[],[f7312,f8774])). 19.90/20.08 fof(f9034,plain,( 19.90/20.08 ( ! [X12,X10,X11] : (and(X11,and(X10,X12)) = and(and(X11,X12),X10)) )), 19.90/20.08 inference(superposition,[],[f8727,f413])). 19.90/20.08 fof(f9174,plain,( 19.90/20.08 ( ! [X385,X384,X386] : (implies(and(X385,X386),X384) = not(and(X385,and(not(X384),X386)))) )), 19.90/20.08 inference(superposition,[],[f439,f8727])). 19.90/20.08 fof(f9377,plain,( 19.90/20.08 ( ! [X21,X19,X20] : (and(X19,and(X21,X20)) = and(and(X19,X21),X20)) )), 19.90/20.08 inference(backward_demodulation,[],[f9034,f8477])). 19.90/20.08 fof(f9452,plain,( 19.90/20.08 ( ! [X6,X7] : (and(X6,X7) = and(X6,and(X7,X6))) )), 19.90/20.08 inference(superposition,[],[f9034,f460])). 19.90/20.08 fof(f9754,plain,( 19.90/20.08 ( ! [X105,X106] : (and(X105,X106) = and(and(X106,X105),and(X105,X106))) )), 19.90/20.08 inference(superposition,[],[f1491,f9452])). 19.90/20.08 fof(f10061,plain,( 19.90/20.08 ( ! [X422,X421,X423] : (implies(and(X421,X422),X423) = not(and(X422,and(X421,not(X423))))) )), 19.90/20.08 inference(superposition,[],[f169,f8496])). 19.90/20.08 fof(f10232,plain,( 19.90/20.08 ( ! [X4,X5] : (and(X5,X4) = and(X4,and(X4,X5))) )), 19.90/20.08 inference(superposition,[],[f8775,f1491])). 19.90/20.08 fof(f26932,plain,( 19.90/20.08 ( ! [X4,X5] : (is_a_theorem(necessarily(or(not(and(X4,X5)),X4)))) )), 19.90/20.08 inference(resolution,[],[f3142,f463])). 19.90/20.08 fof(f27028,plain,( 19.90/20.08 ( ! [X4,X5] : (is_a_theorem(necessarily(or(X4,not(and(X4,X5)))))) )), 19.90/20.08 inference(forward_demodulation,[],[f26932,f847])). 19.90/20.08 fof(f27137,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (is_a_theorem(necessarily(implies(implies(X2,X3),not(and(and(X2,not(X3)),X4)))))) )), 19.90/20.08 inference(superposition,[],[f27028,f196])). 19.90/20.08 fof(f27142,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(implies(X2,X3),not(and(and(X2,not(X3)),X4))))) )), 19.90/20.08 inference(forward_demodulation,[],[f27137,f168])). 19.90/20.08 fof(f27143,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(implies(X2,X3),not(and(not(X3),and(X2,X4)))))) )), 19.90/20.08 inference(forward_demodulation,[],[f27142,f8496])). 19.90/20.08 fof(f27144,plain,( 19.90/20.08 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,X4),X3)))) )), 19.90/20.08 inference(forward_demodulation,[],[f27143,f439])). 19.90/20.08 fof(f28269,plain,( 19.90/20.08 ( ! [X107,X108,X106] : (is_a_theorem(strict_implies(implies(and(X106,X107),X108),implies(and(X107,X106),X108)))) )), 19.90/20.08 inference(superposition,[],[f27144,f9754])). 19.90/20.08 fof(f37466,plain,( 19.90/20.08 ( ! [X21,X19,X20] : (strict_implies(X21,and(not(X19),not(X20))) = necessarily(not(and(X21,or(X19,X20))))) )), 19.90/20.08 inference(superposition,[],[f2962,f172])). 19.90/20.08 fof(f45662,plain,( 19.90/20.08 ( ! [X14,X15,X13] : (~is_a_theorem(strict_implies(implies(and(X13,X14),X15),implies(and(X14,X13),X15))) | implies(and(X13,X14),X15) = implies(and(X14,X13),X15)) )), 19.90/20.08 inference(resolution,[],[f28269,f391])). 19.90/20.08 fof(f45812,plain,( 19.90/20.08 ( ! [X14,X15,X13] : (implies(and(X13,X14),X15) = implies(and(X14,X13),X15)) )), 19.90/20.08 inference(global_subsumption,[],[f28269,f45662])). 19.90/20.08 fof(f46063,plain,( 19.90/20.08 ( ! [X111,X109,X110] : (strict_implies(and(X109,X110),X111) = necessarily(implies(and(X110,X109),X111))) )), 19.90/20.08 inference(superposition,[],[f168,f45812])). 19.90/20.08 fof(f50733,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (strict_implies(and(and(X8,X9),X8),X10) = necessarily(implies(and(X9,X8),X10))) )), 19.90/20.08 inference(superposition,[],[f46063,f10232])). 19.90/20.08 fof(f50737,plain,( 19.90/20.08 ( ! [X23,X21,X22,X20] : (strict_implies(and(and(X21,X22),X20),X23) = necessarily(implies(and(X21,and(X20,X22)),X23))) )), 19.90/20.08 inference(superposition,[],[f46063,f8727])). 19.90/20.08 fof(f50808,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (strict_implies(and(X9,X8),X10) = strict_implies(and(and(X8,X9),X8),X10)) )), 19.90/20.08 inference(forward_demodulation,[],[f50733,f168])). 19.90/20.08 fof(f50809,plain,( 19.90/20.08 ( ! [X10,X8,X9] : (strict_implies(and(X8,X9),X10) = strict_implies(and(X9,X8),X10)) )), 19.90/20.08 inference(forward_demodulation,[],[f50808,f1396])). 19.90/20.08 fof(f50814,plain,( 19.90/20.08 ( ! [X23,X21,X22,X20] : (strict_implies(and(X21,and(X20,X22)),X23) = strict_implies(and(and(X21,X22),X20),X23)) )), 19.90/20.08 inference(forward_demodulation,[],[f50737,f168])). 19.90/20.08 fof(f50815,plain,( 19.90/20.08 ( ! [X23,X21,X22,X20] : (strict_implies(and(X21,and(X20,X22)),X23) = strict_implies(and(X22,and(X21,X20)),X23)) )), 19.90/20.08 inference(forward_demodulation,[],[f50814,f8496])). 19.90/20.08 fof(f57866,plain,( 19.90/20.08 ( ! [X6,X8,X7] : (not(and(X6,implies(not(X7),X8))) = not(and(implies(not(X8),X7),X6))) )), 19.90/20.08 inference(superposition,[],[f672,f195])). 19.90/20.08 fof(f58097,plain,( 19.90/20.08 ( ! [X6,X8,X7] : (not(and(or(X8,X7),X6)) = not(and(X6,implies(not(X7),X8)))) )), 19.90/20.08 inference(forward_demodulation,[],[f57866,f172])). 19.90/20.08 fof(f58098,plain,( 19.90/20.08 ( ! [X6,X8,X7] : (not(and(X6,or(X7,X8))) = not(and(or(X8,X7),X6))) )), 19.90/20.08 inference(forward_demodulation,[],[f58097,f172])). 19.90/20.08 fof(f60393,plain,( 19.90/20.08 ( ! [X4,X5,X3] : (implies(and(not(X3),X5),X4) = implies(and(not(X4),X5),X3)) )), 19.90/20.08 inference(superposition,[],[f9174,f439])). 19.90/20.08 fof(f71538,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(and(implies(X41,not(X41)),X42),not(X41)) = not(and(X42,equiv(X41,not(X41))))) )), 19.90/20.08 inference(superposition,[],[f10061,f618])). 19.90/20.08 fof(f71583,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (implies(and(X0,not(X2)),X1) = implies(and(not(X1),X0),X2)) )), 19.90/20.08 inference(superposition,[],[f10061,f9174])). 19.90/20.08 fof(f172115,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(equiv(X66,not(X66)),X67) = implies(and(not(X67),equiv(X66,not(X66))),not(X66))) )), 19.90/20.08 inference(superposition,[],[f71583,f2016])). 19.90/20.08 fof(f179416,plain,( 19.90/20.08 ( ! [X33,X32] : (is_a_theorem(necessarily(not(and(and(not(X32),not(X33)),or(X32,X33)))))) )), 19.90/20.08 inference(superposition,[],[f462,f37466])). 19.90/20.08 fof(f179512,plain,( 19.90/20.08 ( ! [X397,X399,X398] : (is_a_theorem(necessarily(not(and(and(and(not(X397),not(X398)),X399),or(X397,X398)))))) )), 19.90/20.08 inference(superposition,[],[f179,f37466])). 19.90/20.08 fof(f179683,plain,( 19.90/20.08 ( ! [X33,X32] : (is_a_theorem(necessarily(not(and(or(X33,X32),and(not(X32),not(X33))))))) )), 19.90/20.08 inference(forward_demodulation,[],[f179416,f58098])). 19.90/20.08 fof(f179684,plain,( 19.90/20.08 ( ! [X33,X32] : (is_a_theorem(necessarily(implies(and(or(X33,X32),not(X33)),X32)))) )), 19.90/20.08 inference(forward_demodulation,[],[f179683,f9174])). 19.90/20.08 fof(f179685,plain,( 19.90/20.08 ( ! [X33,X32] : (is_a_theorem(strict_implies(and(or(X33,X32),not(X33)),X32))) )), 19.90/20.08 inference(forward_demodulation,[],[f179684,f168])). 19.90/20.08 fof(f179686,plain,( 19.90/20.08 ( ! [X33,X32] : (is_a_theorem(strict_implies(and(not(X33),or(X33,X32)),X32))) )), 19.90/20.08 inference(forward_demodulation,[],[f179685,f50809])). 19.90/20.08 fof(f179784,plain,( 19.90/20.08 ( ! [X397,X399,X398] : (is_a_theorem(necessarily(not(and(or(X398,X397),and(and(not(X397),not(X398)),X399)))))) )), 19.90/20.08 inference(forward_demodulation,[],[f179512,f58098])). 19.90/20.08 fof(f179785,plain,( 19.90/20.08 ( ! [X397,X399,X398] : (is_a_theorem(necessarily(not(and(or(X398,X397),and(not(X398),and(not(X397),X399))))))) )), 19.90/20.08 inference(forward_demodulation,[],[f179784,f8496])). 19.90/20.08 fof(f179786,plain,( 19.90/20.08 ( ! [X397,X399,X398] : (is_a_theorem(necessarily(implies(and(or(X398,X397),and(not(X397),X399)),X398)))) )), 19.90/20.08 inference(forward_demodulation,[],[f179785,f9174])). 19.90/20.08 fof(f179787,plain,( 19.90/20.08 ( ! [X397,X399,X398] : (is_a_theorem(strict_implies(and(or(X398,X397),and(not(X397),X399)),X398))) )), 19.90/20.08 inference(forward_demodulation,[],[f179786,f168])). 19.90/20.08 fof(f179788,plain,( 19.90/20.08 ( ! [X397,X399,X398] : (is_a_theorem(strict_implies(and(not(X397),and(X399,or(X398,X397))),X398))) )), 19.90/20.08 inference(forward_demodulation,[],[f179787,f50815])). 19.90/20.08 fof(f179963,plain,( 19.90/20.08 ( ! [X19,X17,X18] : (is_a_theorem(strict_implies(and(not(X17),or(X17,and(X18,X19))),X18))) )), 19.90/20.08 inference(resolution,[],[f179686,f3075])). 19.90/20.08 fof(f180984,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(not(X0),and(X1,not(not(X0)))),X0))) )), 19.90/20.08 inference(superposition,[],[f179788,f614])). 19.90/20.08 fof(f181078,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X1,not(not(X0))),X0))) )), 19.90/20.08 inference(forward_demodulation,[],[f180984,f1648])). 19.90/20.08 fof(f181097,plain,( 19.90/20.08 ( ! [X14,X15,X16] : (is_a_theorem(strict_implies(and(X14,not(not(and(X15,X16)))),X16))) )), 19.90/20.08 inference(resolution,[],[f181078,f3077])). 19.90/20.08 fof(f182744,plain,( 19.90/20.08 ( ! [X54,X52,X53] : (is_a_theorem(strict_implies(and(X54,not(implies(X53,X52))),X53))) )), 19.90/20.08 inference(superposition,[],[f181097,f439])). 19.90/20.08 fof(f183555,plain,( 19.90/20.08 ( ! [X87,X85,X86] : (is_a_theorem(strict_implies(and(X87,not(or(X85,X86))),not(X85)))) )), 19.90/20.08 inference(superposition,[],[f182744,f172])). 19.90/20.08 fof(f197031,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(or(X0,and(X0,X1)),X0))) )), 19.90/20.08 inference(superposition,[],[f179963,f1648])). 19.90/20.08 fof(f197232,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(implies(implies(X0,X1),X0),X0))) )), 19.90/20.08 inference(superposition,[],[f197031,f720])). 19.90/20.08 fof(f197235,plain,( 19.90/20.08 ( ! [X8,X9] : (is_a_theorem(strict_implies(implies(implies(X9,X8),not(X8)),not(X8)))) )), 19.90/20.08 inference(superposition,[],[f197031,f721])). 19.90/20.08 fof(f198295,plain,( 19.90/20.08 ( ! [X6,X7] : (and(implies(X6,X7),not(X6)) = not(X6)) )), 19.90/20.08 inference(resolution,[],[f197232,f1793])). 19.90/20.08 fof(f198298,plain,( 19.90/20.08 ( ! [X14,X12,X13] : (~is_a_theorem(strict_implies(X12,implies(implies(X13,X14),X13))) | is_a_theorem(strict_implies(X12,X13))) )), 19.90/20.08 inference(resolution,[],[f197232,f915])). 19.90/20.08 fof(f198299,plain,( 19.90/20.08 ( ! [X15,X16] : (~is_a_theorem(strict_implies(X15,implies(implies(X15,X16),X15))) | implies(implies(X15,X16),X15) = X15) )), 19.90/20.08 inference(resolution,[],[f197232,f391])). 19.90/20.08 fof(f198746,plain,( 19.90/20.08 ( ! [X59,X60] : (and(or(X60,X59),not(not(X59))) = not(not(X59))) )), 19.90/20.08 inference(superposition,[],[f198295,f696])). 19.90/20.08 fof(f198831,plain,( 19.90/20.08 ( ! [X37,X36] : (implies(implies(X36,X37),X36) = not(not(X36))) )), 19.90/20.08 inference(superposition,[],[f169,f198295])). 19.90/20.08 fof(f199026,plain,( 19.90/20.08 ( ! [X629,X628,X630] : (and(X630,not(X628)) = and(implies(X628,X629),and(not(X628),X630))) )), 19.90/20.08 inference(superposition,[],[f8775,f198295])). 19.90/20.08 fof(f199053,plain,( 19.90/20.08 ( ! [X726,X725,X727] : (and(not(X725),X727) = and(implies(X725,X726),and(not(X725),X727))) )), 19.90/20.08 inference(superposition,[],[f9377,f198295])). 19.90/20.08 fof(f199784,plain,( 19.90/20.08 ( ! [X15,X16] : (not(not(X15)) = X15 | ~is_a_theorem(strict_implies(X15,implies(implies(X15,X16),X15)))) )), 19.90/20.08 inference(backward_demodulation,[],[f198831,f198299])). 19.90/20.08 fof(f199785,plain,( 19.90/20.08 ( ! [X12,X13] : (~is_a_theorem(strict_implies(X12,not(not(X13)))) | is_a_theorem(strict_implies(X12,X13))) )), 19.90/20.08 inference(backward_demodulation,[],[f198831,f198298])). 19.90/20.08 fof(f199812,plain,( 19.90/20.08 ( ! [X15] : (~is_a_theorem(strict_implies(X15,not(not(X15)))) | not(not(X15)) = X15) )), 19.90/20.08 inference(forward_demodulation,[],[f199784,f198831])). 19.90/20.08 fof(f202892,plain,( 19.90/20.08 ( ! [X6,X7] : (and(implies(X6,X7),not(not(X7))) = not(not(X7))) )), 19.90/20.08 inference(resolution,[],[f197235,f1793])). 19.90/20.08 fof(f202902,plain,( 19.90/20.08 ( ! [X33,X34] : (~is_a_theorem(strict_implies(not(X33),implies(implies(X34,X33),not(X33)))) | implies(implies(X34,X33),not(X33)) = not(X33)) )), 19.90/20.08 inference(resolution,[],[f197235,f391])). 19.90/20.08 fof(f202998,plain,( 19.90/20.08 ( ! [X33,X34] : (~is_a_theorem(necessarily(or(X33,implies(implies(X34,X33),not(X33))))) | implies(implies(X34,X33),not(X33)) = not(X33)) )), 19.90/20.08 inference(forward_demodulation,[],[f202902,f186])). 19.90/20.08 fof(f203745,plain,( 19.90/20.08 ( ! [X43,X44,X42] : (is_a_theorem(strict_implies(and(X42,not(or(not(X43),X44))),X43))) )), 19.90/20.08 inference(resolution,[],[f199785,f183555])). 19.90/20.08 fof(f207773,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(not(or(not(X0),X1)),X0))) )), 19.90/20.08 inference(superposition,[],[f203745,f460])). 19.90/20.08 fof(f207809,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(necessarily(or(or(not(X0),X1),X0)))) )), 19.90/20.08 inference(forward_demodulation,[],[f207773,f186])). 19.90/20.08 fof(f207810,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(necessarily(or(X0,or(not(X0),X1))))) )), 19.90/20.08 inference(forward_demodulation,[],[f207809,f847])). 19.90/20.08 fof(f207885,plain,( 19.90/20.08 ( ! [X6,X7,X5] : (is_a_theorem(necessarily(or(X5,implies(implies(X6,X7),not(X5)))))) )), 19.90/20.08 inference(superposition,[],[f207810,f720])). 19.90/20.08 fof(f207958,plain,( 19.90/20.08 ( ! [X33,X34] : (implies(implies(X34,X33),not(X33)) = not(X33)) )), 19.90/20.08 inference(subsumption_resolution,[],[f202998,f207885])). 19.90/20.08 fof(f208556,plain,( 19.90/20.08 ( ! [X55] : (implies(not(not(X55)),not(X55)) = not(X55)) )), 19.90/20.08 inference(superposition,[],[f207958,f198831])). 19.90/20.08 fof(f208675,plain,( 19.90/20.08 ( ! [X101,X102,X100] : (strict_implies(X102,and(implies(X100,X101),not(not(X101)))) = necessarily(not(and(X102,not(X101))))) )), 19.90/20.08 inference(superposition,[],[f2962,f207958])). 19.90/20.08 fof(f209764,plain,( 19.90/20.08 ( ! [X101,X102,X100] : (strict_implies(X102,and(implies(X100,X101),not(not(X101)))) = necessarily(implies(X102,X101))) )), 19.90/20.08 inference(forward_demodulation,[],[f208675,f169])). 19.90/20.08 fof(f209765,plain,( 19.90/20.08 ( ! [X101,X102,X100] : (strict_implies(X102,X101) = strict_implies(X102,and(implies(X100,X101),not(not(X101))))) )), 19.90/20.08 inference(forward_demodulation,[],[f209764,f168])). 19.90/20.08 fof(f209766,plain,( 19.90/20.08 ( ! [X101,X102] : (strict_implies(X102,X101) = strict_implies(X102,not(not(X101)))) )), 19.90/20.08 inference(forward_demodulation,[],[f209765,f202892])). 19.90/20.08 fof(f209767,plain,( 19.90/20.08 ( ! [X15] : (~is_a_theorem(strict_implies(X15,X15)) | not(not(X15)) = X15) )), 19.90/20.08 inference(backward_demodulation,[],[f209766,f199812])). 19.90/20.08 fof(f210088,plain,( 19.90/20.08 ( ! [X15] : (not(not(X15)) = X15) )), 19.90/20.08 inference(global_subsumption,[],[f462,f209767])). 19.90/20.08 fof(f210090,plain,( 19.90/20.08 ( ! [X0] : (or(X0,X0) = X0) )), 19.90/20.08 inference(backward_demodulation,[],[f210088,f614])). 19.90/20.08 fof(f210091,plain,( 19.90/20.08 ( ! [X2] : (and(implies(X2,not(X2)),X2) = equiv(X2,not(X2))) )), 19.90/20.08 inference(backward_demodulation,[],[f210088,f618])). 19.90/20.08 fof(f210473,plain,( 19.90/20.08 ( ! [X59,X60] : (and(or(X60,X59),X59) = X59) )), 19.90/20.08 inference(backward_demodulation,[],[f210088,f198746])). 19.90/20.08 fof(f210522,plain,( 19.90/20.08 ( ! [X6,X7] : (and(implies(X6,X7),X7) = X7) )), 19.90/20.08 inference(backward_demodulation,[],[f210088,f202892])). 19.90/20.08 fof(f210593,plain,( 19.90/20.08 ( ! [X55] : (implies(X55,not(X55)) = not(X55)) )), 19.90/20.08 inference(backward_demodulation,[],[f210088,f208556])). 19.90/20.08 fof(f214924,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(and(not(X41),X42),not(X41)) = not(and(X42,equiv(X41,not(X41))))) )), 19.90/20.08 inference(backward_demodulation,[],[f210593,f71538])). 19.90/20.08 fof(f214934,plain,( 19.90/20.08 ( ! [X2] : (and(not(X2),X2) = equiv(X2,not(X2))) )), 19.90/20.08 inference(backward_demodulation,[],[f210593,f210091])). 19.90/20.08 fof(f214998,plain,( 19.90/20.08 ( ! [X2] : (and(X2,not(X2)) = equiv(X2,not(X2))) )), 19.90/20.08 inference(forward_demodulation,[],[f214934,f413])). 19.90/20.08 fof(f215117,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(and(X66,not(X66)),X67) = implies(and(not(X67),and(X66,not(X66))),not(X66))) )), 19.90/20.08 inference(backward_demodulation,[],[f214998,f172115])). 19.90/20.08 fof(f215231,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(and(not(X41),X42),not(X41)) = not(and(X42,and(X41,not(X41))))) )), 19.90/20.08 inference(backward_demodulation,[],[f214998,f214924])). 19.90/20.08 fof(f215535,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(and(X41,X42),X41) = implies(and(not(X41),X42),not(X41))) )), 19.90/20.08 inference(forward_demodulation,[],[f215231,f10061])). 19.90/20.08 fof(f225102,plain,( 19.90/20.08 ( ! [X4,X3] : (and(X3,not(X4)) = implies(implies(X3,X4),and(X3,not(X4)))) )), 19.90/20.08 inference(superposition,[],[f210090,f720])). 19.90/20.08 fof(f225458,plain,( 19.90/20.08 ( ! [X4,X3] : (and(X3,not(X4)) = not(implies(X3,X4))) )), 19.90/20.08 inference(forward_demodulation,[],[f225102,f613])). 19.90/20.08 fof(f225499,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(not(implies(X66,X66)),X67) = implies(and(not(X67),not(implies(X66,X66))),not(X66))) )), 19.90/20.08 inference(backward_demodulation,[],[f225458,f215117])). 19.90/20.08 fof(f225618,plain,( 19.90/20.08 ( ! [X422,X421,X423] : (implies(and(X421,X422),X423) = not(and(X422,not(implies(X421,X423))))) )), 19.90/20.08 inference(backward_demodulation,[],[f225458,f10061])). 19.90/20.08 fof(f226102,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (implies(and(not(X1),X0),X2) = implies(not(implies(X0,X2)),X1)) )), 19.90/20.08 inference(backward_demodulation,[],[f225458,f71583])). 19.90/20.08 fof(f227866,plain,( 19.90/20.08 ( ! [X629,X628,X630] : (and(implies(X628,X629),and(not(X628),X630)) = not(implies(X630,X628))) )), 19.90/20.08 inference(backward_demodulation,[],[f225458,f199026])). 19.90/20.08 fof(f231389,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(not(implies(X66,X66)),X67) = implies(not(implies(not(X67),implies(X66,X66))),not(X66))) )), 19.90/20.08 inference(forward_demodulation,[],[f225499,f225458])). 19.90/20.08 fof(f231390,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(not(implies(X66,X66)),X67) = implies(not(or(X67,implies(X66,X66))),not(X66))) )), 19.90/20.08 inference(forward_demodulation,[],[f231389,f172])). 19.90/20.08 fof(f231391,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(not(or(X67,implies(X66,X66))),not(X66)) = or(implies(X66,X66),X67)) )), 19.90/20.08 inference(forward_demodulation,[],[f231390,f172])). 19.90/20.08 fof(f231757,plain,( 19.90/20.08 ( ! [X422,X421,X423] : (implies(and(X421,X422),X423) = not(not(implies(X422,implies(X421,X423))))) )), 19.90/20.08 inference(forward_demodulation,[],[f225618,f225458])). 19.90/20.08 fof(f231758,plain,( 19.90/20.08 ( ! [X422,X421,X423] : (implies(X422,implies(X421,X423)) = implies(and(X421,X422),X423)) )), 19.90/20.08 inference(forward_demodulation,[],[f231757,f210088])). 19.90/20.08 fof(f231761,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(X42,implies(X41,X41)) = implies(and(not(X41),X42),not(X41))) )), 19.90/20.08 inference(backward_demodulation,[],[f231758,f215535])). 19.90/20.08 fof(f231829,plain,( 19.90/20.08 ( ! [X111,X109,X110] : (strict_implies(and(X109,X110),X111) = necessarily(implies(X109,implies(X110,X111)))) )), 19.90/20.08 inference(backward_demodulation,[],[f231758,f46063])). 19.90/20.08 fof(f232966,plain,( 19.90/20.08 ( ! [X4,X5,X3] : (implies(X5,implies(not(X4),X3)) = implies(and(not(X3),X5),X4)) )), 19.90/20.08 inference(backward_demodulation,[],[f231758,f60393])). 19.90/20.08 fof(f235045,plain,( 19.90/20.08 ( ! [X111,X109,X110] : (strict_implies(X109,implies(X110,X111)) = strict_implies(and(X109,X110),X111)) )), 19.90/20.08 inference(forward_demodulation,[],[f231829,f168])). 19.90/20.08 fof(f235051,plain,( 19.90/20.08 ( ! [X4,X5] : (is_a_theorem(strict_implies(X5,implies(X4,X4)))) )), 19.90/20.08 inference(backward_demodulation,[],[f235045,f429])). 19.90/20.08 fof(f235052,plain,( 19.90/20.08 ( ! [X8,X7,X9] : (is_a_theorem(strict_implies(X7,implies(and(X8,X9),X8)))) )), 19.90/20.08 inference(backward_demodulation,[],[f235045,f3116])). 19.90/20.08 fof(f236004,plain,( 19.90/20.08 ( ! [X0,X1] : (is_a_theorem(strict_implies(X0,implies(X1,and(X1,X0))))) )), 19.90/20.08 inference(backward_demodulation,[],[f235045,f180])). 19.90/20.08 fof(f239693,plain,( 19.90/20.08 ( ! [X8,X7,X9] : (is_a_theorem(strict_implies(X7,implies(X9,implies(X8,X8))))) )), 19.90/20.08 inference(forward_demodulation,[],[f235052,f231758])). 19.90/20.08 fof(f247056,plain,( 19.90/20.08 ( ! [X4,X5,X3] : (implies(X5,or(X4,X3)) = implies(and(not(X3),X5),X4)) )), 19.90/20.08 inference(forward_demodulation,[],[f232966,f172])). 19.90/20.08 fof(f249300,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (implies(and(not(X1),X0),X2) = or(implies(X0,X2),X1)) )), 19.90/20.08 inference(forward_demodulation,[],[f226102,f172])). 19.90/20.08 fof(f249301,plain,( 19.90/20.08 ( ! [X2,X0,X1] : (implies(X0,or(X2,X1)) = or(implies(X0,X2),X1)) )), 19.90/20.08 inference(forward_demodulation,[],[f249300,f247056])). 19.90/20.08 fof(f249310,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(X66,or(X66,X67)) = implies(not(or(X67,implies(X66,X66))),not(X66))) )), 19.90/20.08 inference(backward_demodulation,[],[f249301,f231391])). 19.90/20.08 fof(f255244,plain,( 19.90/20.08 ( ! [X725,X727] : (and(not(X725),X727) = not(implies(X727,X725))) )), 19.90/20.08 inference(backward_demodulation,[],[f227866,f199053])). 19.90/20.08 fof(f255477,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(X42,implies(X41,X41)) = implies(not(implies(X42,X41)),not(X41))) )), 19.90/20.08 inference(backward_demodulation,[],[f255244,f231761])). 19.90/20.08 fof(f273469,plain,( 19.90/20.08 ( ! [X8,X7] : (~is_a_theorem(X7) | is_a_theorem(implies(X8,X8))) )), 19.90/20.08 inference(resolution,[],[f235051,f182])). 19.90/20.08 fof(f273524,plain,( 19.90/20.08 ( ! [X44] : (is_a_theorem(implies(X44,X44))) )), 19.90/20.08 inference(resolution,[],[f273469,f462])). 19.90/20.08 fof(f273835,plain,( 19.90/20.08 ( ! [X8,X7] : (is_a_theorem(implies(X8,and(X8,X7))) | ~is_a_theorem(X7)) )), 19.90/20.08 inference(resolution,[],[f236004,f182])). 19.90/20.08 fof(f279329,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(X0) | ~is_a_theorem(implies(and(X1,X0),X1)) | and(X1,X0) = X1) )), 19.90/20.08 inference(resolution,[],[f273835,f421])). 19.90/20.08 fof(f279460,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(implies(X0,implies(X1,X1))) | ~is_a_theorem(X0) | and(X1,X0) = X1) )), 19.90/20.08 inference(forward_demodulation,[],[f279329,f231758])). 19.90/20.08 fof(f280404,plain,( 19.90/20.08 ( ! [X12,X10,X11] : (~is_a_theorem(X10) | is_a_theorem(implies(X11,implies(X12,X12)))) )), 19.90/20.08 inference(resolution,[],[f239693,f182])). 19.90/20.08 fof(f280452,plain,( 19.90/20.08 ( ! [X0,X1] : (~is_a_theorem(X0) | and(X1,X0) = X1) )), 19.90/20.08 inference(subsumption_resolution,[],[f279460,f280404])). 19.90/20.08 fof(f280486,plain,( 19.90/20.08 ( ! [X8,X7] : (and(X7,implies(X8,X8)) = X7) )), 19.90/20.08 inference(resolution,[],[f280452,f273524])). 19.90/20.08 fof(f282067,plain,( 19.90/20.08 ( ! [X37,X38] : (implies(X38,X38) = implies(X37,implies(X38,X38))) )), 19.90/20.08 inference(superposition,[],[f280486,f210522])). 19.90/20.08 fof(f282075,plain,( 19.90/20.08 ( ! [X57,X58] : (implies(X58,X58) = or(X57,implies(X58,X58))) )), 19.90/20.08 inference(superposition,[],[f280486,f210473])). 19.90/20.08 fof(f282333,plain,( 19.90/20.08 ( ! [X41,X42] : (implies(X41,X41) = implies(not(implies(X42,X41)),not(X41))) )), 19.90/20.08 inference(backward_demodulation,[],[f282067,f255477])). 19.90/20.08 fof(f282372,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(X66,or(X66,X67)) = implies(not(implies(X66,X66)),not(X66))) )), 19.90/20.08 inference(backward_demodulation,[],[f282075,f249310])). 19.90/20.08 fof(f282375,plain,( 19.90/20.08 ( ! [X66,X67] : (implies(X66,X66) = implies(X66,or(X66,X67))) )), 19.90/20.08 inference(forward_demodulation,[],[f282372,f282333])). 19.90/20.08 fof(f282417,plain,( 19.90/20.08 ~is_a_theorem(implies(sK0,sK0))), 19.90/20.08 inference(backward_demodulation,[],[f282375,f174])). 19.90/20.08 fof(f282552,plain,( 19.90/20.08 $false), 19.90/20.08 inference(resolution,[],[f282417,f273524])). 19.90/20.08 % SZS output end Proof for theBenchmark 19.90/20.08 % ------------------------------ 19.90/20.08 % Version: Vampire 4.2 (commit c955596 on 2017-07-21 22:07:53 +0100) 19.90/20.08 % Termination reason: Refutation 19.90/20.08 19.90/20.08 % Memory used [KB]: 296029 19.90/20.08 % Time elapsed: 11.271 s 19.90/20.08 % ------------------------------ 19.90/20.08 % ------------------------------ 19.99/20.09 % Success in time 19.852 s 19.99/20.10 EOF