TSTP Solution File: SEU785^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU785^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.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 : Tue May 21 03:51:31 EDT 2024
% Result : Theorem 0.11s 0.38s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU785^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.34 % Computer : n020.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sun May 19 17:46:08 EDT 2024
% 0.11/0.35 % CPUTime :
% 0.11/0.35 This is a TH0_THM_EQU_NAR problem
% 0.11/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % (21427)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.11/0.37 % (21425)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.11/0.37 % (21426)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.37 % (21427)Instruction limit reached!
% 0.11/0.37 % (21427)------------------------------
% 0.11/0.37 % (21427)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (21427)Termination reason: Unknown
% 0.11/0.37 % (21427)Termination phase: Preprocessing 3
% 0.11/0.37
% 0.11/0.37 % (21427)Memory used [KB]: 1023
% 0.11/0.37 % (21427)Time elapsed: 0.002 s
% 0.11/0.37 % (21427)Instructions burned: 3 (million)
% 0.11/0.37 % (21427)------------------------------
% 0.11/0.37 % (21427)------------------------------
% 0.11/0.37 % (21422)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.37 % (21422)Instruction limit reached!
% 0.11/0.37 % (21422)------------------------------
% 0.11/0.37 % (21422)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (21422)Termination reason: Unknown
% 0.11/0.37 % (21422)Termination phase: Property scanning
% 0.11/0.37
% 0.11/0.37 % (21422)Memory used [KB]: 895
% 0.11/0.37 % (21422)Time elapsed: 0.002 s
% 0.11/0.37 % (21422)Instructions burned: 2 (million)
% 0.11/0.37 % (21422)------------------------------
% 0.11/0.37 % (21422)------------------------------
% 0.11/0.37 % (21423)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.37 % (21423)Instruction limit reached!
% 0.11/0.37 % (21423)------------------------------
% 0.11/0.37 % (21423)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (21423)Termination reason: Unknown
% 0.11/0.37 % (21423)Termination phase: Preprocessing 3
% 0.11/0.37
% 0.11/0.37 % (21423)Memory used [KB]: 895
% 0.11/0.37 % (21423)Time elapsed: 0.003 s
% 0.11/0.37 % (21423)Instructions burned: 3 (million)
% 0.11/0.37 % (21423)------------------------------
% 0.11/0.37 % (21423)------------------------------
% 0.11/0.37 % (21420)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.11/0.37 % (21425)First to succeed.
% 0.11/0.37 % (21420)Instruction limit reached!
% 0.11/0.37 % (21420)------------------------------
% 0.11/0.37 % (21420)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (21420)Termination reason: Unknown
% 0.11/0.37 % (21420)Termination phase: Property scanning
% 0.11/0.37
% 0.11/0.37 % (21420)Memory used [KB]: 1023
% 0.11/0.37 % (21420)Time elapsed: 0.003 s
% 0.11/0.37 % (21420)Instructions burned: 4 (million)
% 0.11/0.37 % (21420)------------------------------
% 0.11/0.37 % (21420)------------------------------
% 0.11/0.37 % (21419)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.37 % (21428)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.11/0.37 % (21426)Instruction limit reached!
% 0.11/0.37 % (21426)------------------------------
% 0.11/0.37 % (21426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.37 % (21426)Termination reason: Unknown
% 0.11/0.37 % (21426)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (21426)Memory used [KB]: 5628
% 0.11/0.37 % (21426)Time elapsed: 0.011 s
% 0.11/0.37 % (21426)Instructions burned: 18 (million)
% 0.11/0.37 % (21426)------------------------------
% 0.11/0.37 % (21426)------------------------------
% 0.11/0.38 % (21425)Refutation found. Thanks to Tanya!
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38 % SZS output start Proof for theBenchmark
% 0.11/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.11/0.38 thf(func_def_1, type, binunion: $i > $i > $i).
% 0.11/0.38 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.11/0.38 thf(func_def_3, type, breln1: $i > $i > $o).
% 0.11/0.38 thf(f108,plain,(
% 0.11/0.38 $false),
% 0.11/0.38 inference(avatar_sat_refutation,[],[f84,f99,f101,f107])).
% 0.11/0.38 thf(f107,plain,(
% 0.11/0.38 ~spl15_3),
% 0.11/0.38 inference(avatar_contradiction_clause,[],[f106])).
% 0.11/0.38 thf(f106,plain,(
% 0.11/0.38 $false | ~spl15_3),
% 0.11/0.38 inference(subsumption_resolution,[],[f105,f49])).
% 0.11/0.38 thf(f49,plain,(
% 0.11/0.38 ((in @ sK9 @ sK5) = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f30,plain,(
% 0.11/0.38 (breln1unionIR = $true) & (((breln1 @ sK5 @ sK6) = $true) & (((breln1 @ sK5 @ sK7) = $true) & ((((in @ sK9 @ sK5) = $true) & ((in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7)) != $true) & (((in @ (kpair @ sK8 @ sK9) @ sK6) = $true) | ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true))) & ((in @ sK8 @ sK5) = $true)))) & (breln1unionIL = $true)),
% 0.11/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f25,f29,f28,f27,f26])).
% 0.11/0.38 thf(f26,plain,(
% 0.11/0.38 ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (((breln1 @ X0 @ X2) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X3 @ X0) = $true)))) => (((breln1 @ sK5 @ sK6) = $true) & ? [X2] : (((breln1 @ sK5 @ X2) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ sK5) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ sK6) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X3 @ sK5) = $true))))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f27,plain,(
% 0.11/0.38 ? [X2] : (((breln1 @ sK5 @ X2) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ sK5) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ sK6) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X3 @ sK5) = $true))) => (((breln1 @ sK5 @ sK7) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ sK5) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ sK7))) & (((in @ (kpair @ X3 @ X4) @ sK6) = $true) | ((in @ (kpair @ X3 @ X4) @ sK7) = $true))) & ((in @ X3 @ sK5) = $true)))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f28,plain,(
% 0.11/0.38 ? [X3] : (? [X4] : (((in @ X4 @ sK5) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (binunion @ sK6 @ sK7))) & (((in @ (kpair @ X3 @ X4) @ sK6) = $true) | ((in @ (kpair @ X3 @ X4) @ sK7) = $true))) & ((in @ X3 @ sK5) = $true)) => (? [X4] : (((in @ X4 @ sK5) = $true) & ((in @ (kpair @ sK8 @ X4) @ (binunion @ sK6 @ sK7)) != $true) & (((in @ (kpair @ sK8 @ X4) @ sK6) = $true) | ((in @ (kpair @ sK8 @ X4) @ sK7) = $true))) & ((in @ sK8 @ sK5) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f29,plain,(
% 0.11/0.38 ? [X4] : (((in @ X4 @ sK5) = $true) & ((in @ (kpair @ sK8 @ X4) @ (binunion @ sK6 @ sK7)) != $true) & (((in @ (kpair @ sK8 @ X4) @ sK6) = $true) | ((in @ (kpair @ sK8 @ X4) @ sK7) = $true))) => (((in @ sK9 @ sK5) = $true) & ((in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7)) != $true) & (((in @ (kpair @ sK8 @ sK9) @ sK6) = $true) | ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true)))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f25,plain,(
% 0.11/0.38 (breln1unionIR = $true) & ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (((breln1 @ X0 @ X2) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ X1) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X3 @ X0) = $true)))) & (breln1unionIL = $true)),
% 0.11/0.38 inference(rectify,[],[f17])).
% 0.11/0.38 thf(f17,plain,(
% 0.11/0.38 (breln1unionIR = $true) & ? [X1,X0] : (((breln1 @ X1 @ X0) = $true) & ? [X2] : (((breln1 @ X1 @ X2) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X1) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ X0) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X3 @ X1) = $true)))) & (breln1unionIL = $true)),
% 0.11/0.38 inference(flattening,[],[f16])).
% 0.11/0.38 thf(f16,plain,(
% 0.11/0.38 (? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) != $true) & (((in @ (kpair @ X3 @ X4) @ X0) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)),
% 0.11/0.38 inference(ennf_transformation,[],[f11])).
% 0.11/0.38 thf(f11,plain,(
% 0.11/0.38 ~((breln1unionIL = $true) => ((breln1unionIR = $true) => ! [X0,X1] : (((breln1 @ X1 @ X0) = $true) => ! [X2] : (((breln1 @ X1 @ X2) = $true) => ! [X3] : (((in @ X3 @ X1) = $true) => ! [X4] : (((in @ X4 @ X1) = $true) => ((((in @ (kpair @ X3 @ X4) @ X0) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) = $true)) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true))))))))),
% 0.11/0.38 inference(fool_elimination,[],[f10])).
% 0.11/0.38 thf(f10,plain,(
% 0.11/0.38 ~(breln1unionIL => (breln1unionIR => ! [X0,X1] : ((breln1 @ X1 @ X0) => ! [X2] : ((breln1 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X1) => (((in @ (kpair @ X3 @ X4) @ X2) | (in @ (kpair @ X3 @ X4) @ X0)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)))))))))),
% 0.11/0.38 inference(rectify,[],[f4])).
% 0.11/0.38 thf(f4,negated_conjecture,(
% 0.11/0.38 ~(breln1unionIL => (breln1unionIR => ! [X1,X0] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => (((in @ (kpair @ X3 @ X4) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)))))))))),
% 0.11/0.38 inference(negated_conjecture,[],[f3])).
% 0.11/0.38 thf(f3,conjecture,(
% 0.11/0.38 breln1unionIL => (breln1unionIR => ! [X1,X0] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => (((in @ (kpair @ X3 @ X4) @ X2) | (in @ (kpair @ X3 @ X4) @ X1)) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionI)).
% 0.11/0.38 thf(f105,plain,(
% 0.11/0.38 ((in @ sK9 @ sK5) != $true) | ~spl15_3),
% 0.11/0.38 inference(subsumption_resolution,[],[f104,f51])).
% 0.11/0.38 thf(f51,plain,(
% 0.11/0.38 ((breln1 @ sK5 @ sK6) = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f104,plain,(
% 0.11/0.38 ((breln1 @ sK5 @ sK6) != $true) | ((in @ sK9 @ sK5) != $true) | ~spl15_3),
% 0.11/0.38 inference(subsumption_resolution,[],[f103,f46])).
% 0.11/0.38 thf(f46,plain,(
% 0.11/0.38 ((in @ sK8 @ sK5) = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f103,plain,(
% 0.11/0.38 ((in @ sK8 @ sK5) != $true) | ((in @ sK9 @ sK5) != $true) | ((breln1 @ sK5 @ sK6) != $true) | ~spl15_3),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f102])).
% 0.11/0.38 thf(f102,plain,(
% 0.11/0.38 ((in @ sK9 @ sK5) != $true) | ((in @ sK8 @ sK5) != $true) | ($true != $true) | ((breln1 @ sK5 @ sK6) != $true) | ~spl15_3),
% 0.11/0.38 inference(superposition,[],[f98,f50])).
% 0.11/0.38 thf(f50,plain,(
% 0.11/0.38 ((breln1 @ sK5 @ sK7) = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f98,plain,(
% 0.11/0.38 ( ! [X0 : $i] : (((breln1 @ X0 @ sK7) != $true) | ((in @ sK9 @ X0) != $true) | ((in @ sK8 @ X0) != $true) | ((breln1 @ X0 @ sK6) != $true)) ) | ~spl15_3),
% 0.11/0.38 inference(avatar_component_clause,[],[f97])).
% 0.11/0.38 thf(f97,plain,(
% 0.11/0.38 spl15_3 <=> ! [X0] : (((breln1 @ X0 @ sK7) != $true) | ((in @ sK8 @ X0) != $true) | ((in @ sK9 @ X0) != $true) | ((breln1 @ X0 @ sK6) != $true))),
% 0.11/0.38 introduced(avatar_definition,[new_symbols(naming,[spl15_3])])).
% 0.11/0.38 thf(f101,plain,(
% 0.11/0.38 spl15_3 | ~spl15_1),
% 0.11/0.38 inference(avatar_split_clause,[],[f100,f77,f97])).
% 0.11/0.38 thf(f77,plain,(
% 0.11/0.38 spl15_1 <=> ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true)),
% 0.11/0.38 introduced(avatar_definition,[new_symbols(naming,[spl15_1])])).
% 0.11/0.38 thf(f100,plain,(
% 0.11/0.38 ( ! [X0 : $i] : (((breln1 @ X0 @ sK7) != $true) | ((in @ sK8 @ X0) != $true) | ((breln1 @ X0 @ sK6) != $true) | ((in @ sK9 @ X0) != $true)) ) | ~spl15_1),
% 0.11/0.38 inference(subsumption_resolution,[],[f89,f79])).
% 0.11/0.38 thf(f79,plain,(
% 0.11/0.38 ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true) | ~spl15_1),
% 0.11/0.38 inference(avatar_component_clause,[],[f77])).
% 0.11/0.38 thf(f89,plain,(
% 0.11/0.38 ( ! [X0 : $i] : (((breln1 @ X0 @ sK7) != $true) | ((in @ sK9 @ X0) != $true) | ((in @ sK8 @ X0) != $true) | ((in @ (kpair @ sK8 @ sK9) @ sK7) != $true) | ((breln1 @ X0 @ sK6) != $true)) )),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f88])).
% 0.11/0.38 thf(f88,plain,(
% 0.11/0.38 ( ! [X0 : $i] : (((in @ (kpair @ sK8 @ sK9) @ sK7) != $true) | ((breln1 @ X0 @ sK7) != $true) | ((in @ sK9 @ X0) != $true) | ($true != $true) | ((in @ sK8 @ X0) != $true) | ((breln1 @ X0 @ sK6) != $true)) )),
% 0.11/0.38 inference(superposition,[],[f48,f75])).
% 0.11/0.38 thf(f75,plain,(
% 0.11/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((breln1 @ X0 @ X2) != $true) | ((in @ X4 @ X0) != $true) | ((in @ X3 @ X0) != $true) | ((breln1 @ X0 @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) )),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f67])).
% 0.11/0.38 thf(f67,plain,(
% 0.11/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != $true) | ((in @ X3 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((breln1 @ X0 @ X2) != $true) | ((breln1 @ X0 @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true) | ((in @ X4 @ X0) != $true)) )),
% 0.11/0.38 inference(definition_unfolding,[],[f59,f52])).
% 0.11/0.38 thf(f52,plain,(
% 0.11/0.38 (breln1unionIR = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f59,plain,(
% 0.11/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((breln1 @ X0 @ X1) != $true) | ((in @ X3 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true) | ((breln1 @ X0 @ X2) != $true) | (breln1unionIR != $true)) )),
% 0.11/0.38 inference(cnf_transformation,[],[f37])).
% 0.11/0.38 thf(f37,plain,(
% 0.11/0.38 (! [X0,X1] : (((breln1 @ X0 @ X1) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true))) | ((breln1 @ X0 @ X2) != $true))) | (breln1unionIR != $true)) & ((breln1unionIR = $true) | (((breln1 @ sK10 @ sK11) = $true) & ((((in @ sK13 @ sK10) = $true) & (((in @ (kpair @ sK13 @ sK14) @ (binunion @ sK11 @ sK12)) != $true) & ((in @ sK14 @ sK10) = $true) & ((in @ (kpair @ sK13 @ sK14) @ sK12) = $true))) & ((breln1 @ sK10 @ sK12) = $true))))),
% 0.11/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14])],[f32,f36,f35,f34,f33])).
% 0.11/0.38 thf(f33,plain,(
% 0.11/0.38 ? [X5,X6] : (((breln1 @ X5 @ X6) = $true) & ? [X7] : (? [X8] : (((in @ X8 @ X5) = $true) & ? [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) & ((in @ X9 @ X5) = $true) & ((in @ (kpair @ X8 @ X9) @ X7) = $true))) & ((breln1 @ X5 @ X7) = $true))) => (((breln1 @ sK10 @ sK11) = $true) & ? [X7] : (? [X8] : (((in @ X8 @ sK10) = $true) & ? [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ sK11 @ X7)) != $true) & ((in @ X9 @ sK10) = $true) & ((in @ (kpair @ X8 @ X9) @ X7) = $true))) & ((breln1 @ sK10 @ X7) = $true)))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f34,plain,(
% 0.11/0.38 ? [X7] : (? [X8] : (((in @ X8 @ sK10) = $true) & ? [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ sK11 @ X7)) != $true) & ((in @ X9 @ sK10) = $true) & ((in @ (kpair @ X8 @ X9) @ X7) = $true))) & ((breln1 @ sK10 @ X7) = $true)) => (? [X8] : (((in @ X8 @ sK10) = $true) & ? [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ sK11 @ sK12)) != $true) & ((in @ X9 @ sK10) = $true) & ((in @ (kpair @ X8 @ X9) @ sK12) = $true))) & ((breln1 @ sK10 @ sK12) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f35,plain,(
% 0.11/0.38 ? [X8] : (((in @ X8 @ sK10) = $true) & ? [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ sK11 @ sK12)) != $true) & ((in @ X9 @ sK10) = $true) & ((in @ (kpair @ X8 @ X9) @ sK12) = $true))) => (((in @ sK13 @ sK10) = $true) & ? [X9] : (((in @ (kpair @ sK13 @ X9) @ (binunion @ sK11 @ sK12)) != $true) & ((in @ X9 @ sK10) = $true) & ($true = (in @ (kpair @ sK13 @ X9) @ sK12))))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f36,plain,(
% 0.11/0.38 ? [X9] : (((in @ (kpair @ sK13 @ X9) @ (binunion @ sK11 @ sK12)) != $true) & ((in @ X9 @ sK10) = $true) & ($true = (in @ (kpair @ sK13 @ X9) @ sK12))) => (((in @ (kpair @ sK13 @ sK14) @ (binunion @ sK11 @ sK12)) != $true) & ((in @ sK14 @ sK10) = $true) & ((in @ (kpair @ sK13 @ sK14) @ sK12) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f32,plain,(
% 0.11/0.38 (! [X0,X1] : (((breln1 @ X0 @ X1) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2)) = $true) | ((in @ X4 @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true))) | ((breln1 @ X0 @ X2) != $true))) | (breln1unionIR != $true)) & ((breln1unionIR = $true) | ? [X5,X6] : (((breln1 @ X5 @ X6) = $true) & ? [X7] : (? [X8] : (((in @ X8 @ X5) = $true) & ? [X9] : (((in @ (kpair @ X8 @ X9) @ (binunion @ X6 @ X7)) != $true) & ((in @ X9 @ X5) = $true) & ((in @ (kpair @ X8 @ X9) @ X7) = $true))) & ((breln1 @ X5 @ X7) = $true))))),
% 0.11/0.38 inference(rectify,[],[f31])).
% 0.11/0.38 thf(f31,plain,(
% 0.11/0.38 (! [X1,X0] : (((breln1 @ X1 @ X0) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true))) | ((breln1 @ X1 @ X2) != $true))) | (breln1unionIR != $true)) & ((breln1unionIR = $true) | ? [X1,X0] : (((breln1 @ X1 @ X0) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) != $true) & ((in @ X4 @ X1) = $true) & ((in @ (kpair @ X3 @ X4) @ X2) = $true))) & ((breln1 @ X1 @ X2) = $true))))),
% 0.11/0.38 inference(nnf_transformation,[],[f13])).
% 0.11/0.38 thf(f13,plain,(
% 0.11/0.38 ! [X1,X0] : (((breln1 @ X1 @ X0) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) | ((in @ X4 @ X1) != $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true))) | ((breln1 @ X1 @ X2) != $true))) <=> (breln1unionIR = $true)),
% 0.11/0.38 inference(flattening,[],[f12])).
% 0.11/0.38 thf(f12,plain,(
% 0.11/0.38 (breln1unionIR = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) | ((in @ (kpair @ X3 @ X4) @ X2) != $true)) | ((in @ X4 @ X1) != $true)) | ((in @ X3 @ X1) != $true)) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true))),
% 0.11/0.38 inference(ennf_transformation,[],[f7])).
% 0.11/0.38 thf(f7,plain,(
% 0.11/0.38 (breln1unionIR = $true) <=> ! [X0,X1] : (((breln1 @ X1 @ X0) = $true) => ! [X2] : (((breln1 @ X1 @ X2) = $true) => ! [X3] : (((in @ X3 @ X1) = $true) => ! [X4] : (((in @ X4 @ X1) = $true) => (((in @ (kpair @ X3 @ X4) @ X2) = $true) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true))))))),
% 0.11/0.38 inference(fool_elimination,[],[f6])).
% 0.11/0.38 thf(f6,plain,(
% 0.11/0.38 (! [X0,X1] : ((breln1 @ X1 @ X0) => ! [X2] : ((breln1 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))))))) = breln1unionIR)),
% 0.11/0.38 inference(rectify,[],[f2])).
% 0.11/0.38 thf(f2,axiom,(
% 0.11/0.38 (! [X1,X0] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))) = breln1unionIR)),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIR)).
% 0.11/0.38 thf(f48,plain,(
% 0.11/0.38 ((in @ (kpair @ sK8 @ sK9) @ (binunion @ sK6 @ sK7)) != $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f99,plain,(
% 0.11/0.38 ~spl15_2 | spl15_3),
% 0.11/0.38 inference(avatar_split_clause,[],[f86,f97,f81])).
% 0.11/0.38 thf(f81,plain,(
% 0.11/0.38 spl15_2 <=> ((in @ (kpair @ sK8 @ sK9) @ sK6) = $true)),
% 0.11/0.38 introduced(avatar_definition,[new_symbols(naming,[spl15_2])])).
% 0.11/0.38 thf(f86,plain,(
% 0.11/0.38 ( ! [X0 : $i] : (((breln1 @ X0 @ sK7) != $true) | ((breln1 @ X0 @ sK6) != $true) | ((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | ((in @ sK9 @ X0) != $true) | ((in @ sK8 @ X0) != $true)) )),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f85])).
% 0.11/0.38 thf(f85,plain,(
% 0.11/0.38 ( ! [X0 : $i] : (((breln1 @ X0 @ sK7) != $true) | ((in @ sK8 @ X0) != $true) | ((in @ sK9 @ X0) != $true) | ((in @ (kpair @ sK8 @ sK9) @ sK6) != $true) | ((breln1 @ X0 @ sK6) != $true) | ($true != $true)) )),
% 0.11/0.38 inference(superposition,[],[f48,f74])).
% 0.11/0.38 thf(f74,plain,(
% 0.11/0.38 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)) = $true) | ((in @ X9 @ X6) != $true) | ((breln1 @ X6 @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((in @ X8 @ X6) != $true) | ((breln1 @ X6 @ X7) != $true)) )),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f66])).
% 0.11/0.38 thf(f66,plain,(
% 0.11/0.38 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((breln1 @ X6 @ X7) != $true) | ((in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)) = $true) | ($true != $true) | ((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((in @ X8 @ X6) != $true) | ((breln1 @ X6 @ X5) != $true) | ((in @ X9 @ X6) != $true)) )),
% 0.11/0.38 inference(definition_unfolding,[],[f38,f45])).
% 0.11/0.38 thf(f45,plain,(
% 0.11/0.38 (breln1unionIL = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 thf(f38,plain,(
% 0.11/0.38 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)) = $true) | ((in @ X9 @ X6) != $true) | ((in @ X8 @ X6) != $true) | ((breln1 @ X6 @ X7) != $true) | ((breln1 @ X6 @ X5) != $true) | (breln1unionIL != $true)) )),
% 0.11/0.38 inference(cnf_transformation,[],[f24])).
% 0.11/0.38 thf(f24,plain,(
% 0.11/0.38 ((breln1unionIL = $true) | ((((((in @ (kpair @ sK3 @ sK4) @ sK0) = $true) & ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK0 @ sK2)) != $true) & ((in @ sK4 @ sK1) = $true)) & ((in @ sK3 @ sK1) = $true)) & ((breln1 @ sK1 @ sK2) = $true)) & ((breln1 @ sK1 @ sK0) = $true))) & (! [X5,X6] : (! [X7] : (! [X8] : (! [X9] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)) = $true) | ((in @ X9 @ X6) != $true)) | ((in @ X8 @ X6) != $true)) | ((breln1 @ X6 @ X7) != $true)) | ((breln1 @ X6 @ X5) != $true)) | (breln1unionIL != $true))),
% 0.11/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f23,f22,f21,f20])).
% 0.11/0.38 thf(f20,plain,(
% 0.11/0.38 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) != $true) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) => (? [X2] : (? [X3] : (? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ sK0)) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ X2)) != $true) & ((in @ X4 @ sK1) = $true)) & ((in @ X3 @ sK1) = $true)) & ((breln1 @ sK1 @ X2) = $true)) & ((breln1 @ sK1 @ sK0) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f21,plain,(
% 0.11/0.38 ? [X2] : (? [X3] : (? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ sK0)) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ X2)) != $true) & ((in @ X4 @ sK1) = $true)) & ((in @ X3 @ sK1) = $true)) & ((breln1 @ sK1 @ X2) = $true)) => (? [X3] : (? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ sK0)) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ sK2)) != $true) & ((in @ X4 @ sK1) = $true)) & ((in @ X3 @ sK1) = $true)) & ((breln1 @ sK1 @ sK2) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f22,plain,(
% 0.11/0.38 ? [X3] : (? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ sK0)) & ((in @ (kpair @ X3 @ X4) @ (binunion @ sK0 @ sK2)) != $true) & ((in @ X4 @ sK1) = $true)) & ((in @ X3 @ sK1) = $true)) => (? [X4] : (((in @ (kpair @ sK3 @ X4) @ sK0) = $true) & ((in @ (kpair @ sK3 @ X4) @ (binunion @ sK0 @ sK2)) != $true) & ((in @ X4 @ sK1) = $true)) & ((in @ sK3 @ sK1) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f23,plain,(
% 0.11/0.38 ? [X4] : (((in @ (kpair @ sK3 @ X4) @ sK0) = $true) & ((in @ (kpair @ sK3 @ X4) @ (binunion @ sK0 @ sK2)) != $true) & ((in @ X4 @ sK1) = $true)) => (((in @ (kpair @ sK3 @ sK4) @ sK0) = $true) & ((in @ (kpair @ sK3 @ sK4) @ (binunion @ sK0 @ sK2)) != $true) & ((in @ sK4 @ sK1) = $true))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f19,plain,(
% 0.11/0.38 ((breln1unionIL = $true) | ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) != $true) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true))) & (! [X5,X6] : (! [X7] : (! [X8] : (! [X9] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((in @ (kpair @ X8 @ X9) @ (binunion @ X5 @ X7)) = $true) | ((in @ X9 @ X6) != $true)) | ((in @ X8 @ X6) != $true)) | ((breln1 @ X6 @ X7) != $true)) | ((breln1 @ X6 @ X5) != $true)) | (breln1unionIL != $true))),
% 0.11/0.38 inference(rectify,[],[f18])).
% 0.11/0.38 thf(f18,plain,(
% 0.11/0.38 ((breln1unionIL = $true) | ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ X0) = $true) & ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) != $true) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true))) & (! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) | ((in @ X4 @ X1) != $true)) | ((in @ X3 @ X1) != $true)) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true)) | (breln1unionIL != $true))),
% 0.11/0.38 inference(nnf_transformation,[],[f15])).
% 0.11/0.38 thf(f15,plain,(
% 0.11/0.38 (breln1unionIL = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) | ((in @ X4 @ X1) != $true)) | ((in @ X3 @ X1) != $true)) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true))),
% 0.11/0.38 inference(flattening,[],[f14])).
% 0.11/0.38 thf(f14,plain,(
% 0.11/0.38 ! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : ((((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true) | ((in @ (kpair @ X3 @ X4) @ X0) != $true)) | ((in @ X4 @ X1) != $true)) | ((in @ X3 @ X1) != $true)) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true)) <=> (breln1unionIL = $true)),
% 0.11/0.38 inference(ennf_transformation,[],[f9])).
% 0.11/0.38 thf(f9,plain,(
% 0.11/0.38 ! [X0,X1] : (((breln1 @ X1 @ X0) = $true) => ! [X2] : (((breln1 @ X1 @ X2) = $true) => ! [X3] : (((in @ X3 @ X1) = $true) => ! [X4] : (((in @ X4 @ X1) = $true) => (((in @ (kpair @ X3 @ X4) @ X0) = $true) => ((in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2)) = $true)))))) <=> (breln1unionIL = $true)),
% 0.11/0.38 inference(fool_elimination,[],[f8])).
% 0.11/0.38 thf(f8,plain,(
% 0.11/0.38 (breln1unionIL = ! [X0,X1] : ((breln1 @ X1 @ X0) => ! [X2] : ((breln1 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X0) => (in @ (kpair @ X3 @ X4) @ (binunion @ X0 @ X2))))))))),
% 0.11/0.38 inference(rectify,[],[f1])).
% 0.11/0.38 thf(f1,axiom,(
% 0.11/0.38 (breln1unionIL = ! [X1,X0] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ (binunion @ X1 @ X2))))))))),
% 0.11/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIL)).
% 0.11/0.38 thf(f84,plain,(
% 0.11/0.38 spl15_1 | spl15_2),
% 0.11/0.38 inference(avatar_split_clause,[],[f47,f81,f77])).
% 0.11/0.38 thf(f47,plain,(
% 0.11/0.38 ((in @ (kpair @ sK8 @ sK9) @ sK7) = $true) | ((in @ (kpair @ sK8 @ sK9) @ sK6) = $true)),
% 0.11/0.38 inference(cnf_transformation,[],[f30])).
% 0.11/0.38 % SZS output end Proof for theBenchmark
% 0.11/0.38 % (21425)------------------------------
% 0.11/0.38 % (21425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.38 % (21425)Termination reason: Refutation
% 0.11/0.38
% 0.11/0.38 % (21425)Memory used [KB]: 5628
% 0.11/0.38 % (21425)Time elapsed: 0.010 s
% 0.11/0.38 % (21425)Instructions burned: 8 (million)
% 0.11/0.38 % (21425)------------------------------
% 0.11/0.38 % (21425)------------------------------
% 0.11/0.38 % (21418)Success in time 0.021 s
% 0.11/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------