TSTP Solution File: SET956+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:26:11 EDT 2022
% Result : Theorem 0.18s 0.53s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 12 unt; 0 def)
% Number of atoms : 135 ( 19 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 141 ( 51 ~; 37 |; 41 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 134 ( 109 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f155,plain,
$false,
inference(subsumption_resolution,[],[f154,f44]) ).
fof(f44,plain,
~ subset(sK1,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( subset(sK1,cartesian_product2(sK2,sK4))
& ~ subset(sK1,sK3)
& ! [X4,X5] :
( in(ordered_pair(X5,X4),sK3)
| ~ in(ordered_pair(X5,X4),sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f26,f27]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3] :
( subset(X0,cartesian_product2(X1,X3))
& ~ subset(X0,X2)
& ! [X4,X5] :
( in(ordered_pair(X5,X4),X2)
| ~ in(ordered_pair(X5,X4),X0) ) )
=> ( subset(sK1,cartesian_product2(sK2,sK4))
& ~ subset(sK1,sK3)
& ! [X5,X4] :
( in(ordered_pair(X5,X4),sK3)
| ~ in(ordered_pair(X5,X4),sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
? [X0,X1,X2,X3] :
( subset(X0,cartesian_product2(X1,X3))
& ~ subset(X0,X2)
& ! [X4,X5] :
( in(ordered_pair(X5,X4),X2)
| ~ in(ordered_pair(X5,X4),X0) ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
? [X2,X3,X1,X0] :
( subset(X2,cartesian_product2(X3,X0))
& ~ subset(X2,X1)
& ! [X4,X5] :
( in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X5,X4),X2) ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
? [X0,X3,X1,X2] :
( ~ subset(X2,X1)
& subset(X2,cartesian_product2(X3,X0))
& ! [X4,X5] :
( in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X5,X4),X2) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X0,X3,X1,X2] :
( ( subset(X2,cartesian_product2(X3,X0))
& ! [X4,X5] :
( in(ordered_pair(X5,X4),X2)
=> in(ordered_pair(X5,X4),X1) ) )
=> subset(X2,X1) ),
inference(rectify,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X2,X3,X0,X1] :
( ( subset(X0,cartesian_product2(X1,X2))
& ! [X5,X4] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) ) )
=> subset(X0,X3) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X2,X3,X0,X1] :
( ( subset(X0,cartesian_product2(X1,X2))
& ! [X5,X4] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) ) )
=> subset(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(f154,plain,
subset(sK1,sK3),
inference(resolution,[],[f147,f50]) ).
fof(f50,plain,
! [X0,X1] :
( in(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ~ in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(X3,X1)
& in(X3,X0) )
=> ( ~ in(sK7(X0,X1),X1)
& in(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ~ in(X3,X1)
& in(X3,X0) ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f147,plain,
~ in(sK7(sK1,sK3),sK1),
inference(subsumption_resolution,[],[f145,f44]) ).
fof(f145,plain,
( subset(sK1,sK3)
| ~ in(sK7(sK1,sK3),sK1) ),
inference(resolution,[],[f111,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f111,plain,
( in(sK7(sK1,sK3),sK3)
| ~ in(sK7(sK1,sK3),sK1) ),
inference(superposition,[],[f59,f103]) ).
fof(f103,plain,
sK7(sK1,sK3) = unordered_pair(singleton(sK6(sK2,sK4,sK7(sK1,sK3))),unordered_pair(sK6(sK2,sK4,sK7(sK1,sK3)),sK5(sK2,sK4,sK7(sK1,sK3)))),
inference(resolution,[],[f94,f44]) ).
fof(f94,plain,
! [X0] :
( subset(sK1,X0)
| sK7(sK1,X0) = unordered_pair(singleton(sK6(sK2,sK4,sK7(sK1,X0))),unordered_pair(sK6(sK2,sK4,sK7(sK1,X0)),sK5(sK2,sK4,sK7(sK1,X0)))) ),
inference(resolution,[],[f86,f50]) ).
fof(f86,plain,
! [X0] :
( ~ in(X0,sK1)
| unordered_pair(singleton(sK6(sK2,sK4,X0)),unordered_pair(sK6(sK2,sK4,X0),sK5(sK2,sK4,X0))) = X0 ),
inference(forward_demodulation,[],[f84,f54]) ).
fof(f54,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f84,plain,
! [X0] :
( unordered_pair(unordered_pair(sK6(sK2,sK4,X0),sK5(sK2,sK4,X0)),singleton(sK6(sK2,sK4,X0))) = X0
| ~ in(X0,sK1) ),
inference(resolution,[],[f57,f45]) ).
fof(f45,plain,
subset(sK1,cartesian_product2(sK2,sK4)),
inference(cnf_transformation,[],[f28]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cartesian_product2(X0,X1))
| ~ in(X2,X3)
| unordered_pair(unordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)),singleton(sK6(X0,X1,X2))) = X2 ),
inference(definition_unfolding,[],[f47,f42]) ).
fof(f42,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cartesian_product2(X0,X1))
| ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)) = X2
| ~ in(X2,X3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ subset(X3,cartesian_product2(X0,X1))
| ( in(sK6(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1)
& ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)) = X2 )
| ~ in(X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X4,X5] :
( in(X5,X0)
& in(X4,X1)
& ordered_pair(X5,X4) = X2 )
=> ( in(sK6(X0,X1,X2),X0)
& in(sK5(X0,X1,X2),X1)
& ordered_pair(sK6(X0,X1,X2),sK5(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ subset(X3,cartesian_product2(X0,X1))
| ? [X4,X5] :
( in(X5,X0)
& in(X4,X1)
& ordered_pair(X5,X4) = X2 )
| ~ in(X2,X3) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X2,X3,X1] :
( ~ subset(X1,cartesian_product2(X0,X2))
| ? [X5,X4] :
( in(X4,X0)
& in(X5,X2)
& ordered_pair(X4,X5) = X3 )
| ~ in(X3,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X2,X0,X3] :
~ ( in(X3,X1)
& subset(X1,cartesian_product2(X0,X2))
& ! [X5,X4] :
~ ( in(X4,X0)
& in(X5,X2)
& ordered_pair(X4,X5) = X3 ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0,X2,X3] :
~ ( in(X3,X0)
& ! [X4,X5] :
~ ( in(X5,X2)
& ordered_pair(X4,X5) = X3
& in(X4,X1) )
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f59,plain,
! [X4,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sK3)
| ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sK1) ),
inference(forward_demodulation,[],[f58,f54]) ).
fof(f58,plain,
! [X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sK1)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sK3) ),
inference(forward_demodulation,[],[f56,f54]) ).
fof(f56,plain,
! [X4,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sK1)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sK3) ),
inference(definition_unfolding,[],[f43,f42,f42]) ).
fof(f43,plain,
! [X4,X5] :
( in(ordered_pair(X5,X4),sK3)
| ~ in(ordered_pair(X5,X4),sK1) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 14:53:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.50 % (29832)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.50 % (29833)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50 % (29835)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.51 % (29823)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51 % (29831)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.51 % (29823)Refutation not found, incomplete strategy% (29823)------------------------------
% 0.18/0.51 % (29823)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (29823)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (29823)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.51
% 0.18/0.51 % (29823)Memory used [KB]: 5373
% 0.18/0.51 % (29823)Time elapsed: 0.115 s
% 0.18/0.51 % (29823)Instructions burned: 2 (million)
% 0.18/0.51 % (29823)------------------------------
% 0.18/0.51 % (29823)------------------------------
% 0.18/0.51 % (29851)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.18/0.51 % (29830)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.51 % (29836)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.52 % (29825)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52 % (29830)Instruction limit reached!
% 0.18/0.52 % (29830)------------------------------
% 0.18/0.52 % (29830)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52 % (29830)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52 % (29830)Termination reason: Unknown
% 0.18/0.52 % (29830)Termination phase: Blocked clause elimination
% 0.18/0.52
% 0.18/0.52 % (29830)Memory used [KB]: 895
% 0.18/0.52 % (29830)Time elapsed: 0.004 s
% 0.18/0.52 % (29830)Instructions burned: 2 (million)
% 0.18/0.52 % (29830)------------------------------
% 0.18/0.52 % (29830)------------------------------
% 0.18/0.52 % (29834)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.52 % (29822)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.52 % (29824)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.52 % (29826)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52 TRYING [1]
% 0.18/0.52 TRYING [2]
% 0.18/0.52 TRYING [3]
% 0.18/0.52 % (29824)First to succeed.
% 0.18/0.52 % (29843)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.18/0.52 % (29832)Also succeeded, but the first one will report.
% 0.18/0.52 % (29845)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.18/0.53 % (29824)Refutation found. Thanks to Tanya!
% 0.18/0.53 % SZS status Theorem for theBenchmark
% 0.18/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.53 % (29824)------------------------------
% 0.18/0.53 % (29824)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.53 % (29824)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.53 % (29824)Termination reason: Refutation
% 0.18/0.53
% 0.18/0.53 % (29824)Memory used [KB]: 1023
% 0.18/0.53 % (29824)Time elapsed: 0.126 s
% 0.18/0.53 % (29824)Instructions burned: 6 (million)
% 0.18/0.53 % (29824)------------------------------
% 0.18/0.53 % (29824)------------------------------
% 0.18/0.53 % (29821)Success in time 0.182 s
%------------------------------------------------------------------------------