TSTP Solution File: SEU651^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU651^2 : 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 : n008.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 03:50:20 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU651^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % 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
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:32:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (11935)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (11936)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)
% 0.14/0.37 % (11937)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.37 % (11940)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)
% 0.14/0.37 % (11941)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (11938)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (11939)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)
% 0.14/0.37 % (11942)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)
% 0.14/0.37 % (11938)Instruction limit reached!
% 0.14/0.37 % (11938)------------------------------
% 0.14/0.37 % (11938)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11938)Termination reason: Unknown
% 0.14/0.37 % (11939)Instruction limit reached!
% 0.14/0.37 % (11939)------------------------------
% 0.14/0.37 % (11939)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11939)Termination reason: Unknown
% 0.14/0.37 % (11939)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (11939)Memory used [KB]: 895
% 0.14/0.37 % (11939)Time elapsed: 0.003 s
% 0.14/0.37 % (11939)Instructions burned: 3 (million)
% 0.14/0.37 % (11939)------------------------------
% 0.14/0.37 % (11939)------------------------------
% 0.14/0.37 % (11938)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (11938)Memory used [KB]: 895
% 0.14/0.37 % (11938)Time elapsed: 0.003 s
% 0.14/0.37 % (11938)Instructions burned: 3 (million)
% 0.14/0.37 % (11938)------------------------------
% 0.14/0.37 % (11938)------------------------------
% 0.14/0.37 % (11942)Instruction limit reached!
% 0.14/0.37 % (11942)------------------------------
% 0.14/0.37 % (11942)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11942)Termination reason: Unknown
% 0.14/0.37 % (11942)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (11942)Memory used [KB]: 5500
% 0.14/0.37 % (11942)Time elapsed: 0.004 s
% 0.14/0.37 % (11942)Instructions burned: 3 (million)
% 0.14/0.37 % (11942)------------------------------
% 0.14/0.37 % (11942)------------------------------
% 0.14/0.38 % (11936)Instruction limit reached!
% 0.14/0.38 % (11936)------------------------------
% 0.14/0.38 % (11936)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (11936)Termination reason: Unknown
% 0.14/0.38 % (11936)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (11936)Memory used [KB]: 5500
% 0.14/0.38 % (11936)Time elapsed: 0.005 s
% 0.14/0.38 % (11936)Instructions burned: 4 (million)
% 0.14/0.38 % (11936)------------------------------
% 0.14/0.38 % (11936)------------------------------
% 0.14/0.38 % (11940)First to succeed.
% 0.14/0.38 % (11941)Also succeeded, but the first one will report.
% 0.14/0.38 % (11940)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.38 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.14/0.38 thf(f77,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(subsumption_resolution,[],[f76,f42])).
% 0.14/0.38 thf(f42,plain,(
% 0.14/0.38 (sK6 != sK7)),
% 0.14/0.38 inference(cnf_transformation,[],[f32])).
% 0.14/0.38 thf(f32,plain,(
% 0.14/0.38 (uniqinunit = $true) & (setukpairinjR12 = $true) & (secondinupair = $true) & (((setadjoin @ (setadjoin @ sK9 @ emptyset) @ (setadjoin @ (setadjoin @ sK9 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) @ emptyset))) & (sK6 != sK7) & (sK9 = sK7))),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f30,f31])).
% 0.14/0.38 thf(f31,plain,(
% 0.14/0.38 ? [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) & (X0 != X1) & (X1 = X3)) => (((setadjoin @ (setadjoin @ sK9 @ emptyset) @ (setadjoin @ (setadjoin @ sK9 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) @ emptyset))) & (sK6 != sK7) & (sK9 = sK7))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f30,plain,(
% 0.14/0.38 (uniqinunit = $true) & (setukpairinjR12 = $true) & (secondinupair = $true) & ? [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) & (X0 != X1) & (X1 = X3))),
% 0.14/0.38 inference(rectify,[],[f17])).
% 0.14/0.38 thf(f17,plain,(
% 0.14/0.38 (uniqinunit = $true) & (setukpairinjR12 = $true) & (secondinupair = $true) & ? [X0,X2,X1,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) & (X0 != X2) & (X2 = X3))),
% 0.14/0.38 inference(flattening,[],[f16])).
% 0.14/0.38 thf(f16,plain,(
% 0.14/0.38 ((? [X2,X1,X0,X3] : (((X0 != X2) & (X2 = X3)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) & (setukpairinjR12 = $true)) & (secondinupair = $true)) & (uniqinunit = $true)),
% 0.14/0.38 inference(ennf_transformation,[],[f12])).
% 0.14/0.38 thf(f12,plain,(
% 0.14/0.38 ~((uniqinunit = $true) => ((secondinupair = $true) => ((setukpairinjR12 = $true) => ! [X2,X1,X0,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => ((X2 = X3) => (X0 = X2))))))),
% 0.14/0.38 inference(fool_elimination,[],[f11])).
% 0.14/0.38 thf(f11,plain,(
% 0.14/0.38 ~(uniqinunit => (secondinupair => (setukpairinjR12 => ! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => ((X2 = X3) => (X0 = X2))))))),
% 0.14/0.38 inference(rectify,[],[f5])).
% 0.14/0.38 thf(f5,negated_conjecture,(
% 0.14/0.38 ~(uniqinunit => (secondinupair => (setukpairinjR12 => ! [X1,X0,X3,X2] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X2 = X3) => (X1 = X3))))))),
% 0.14/0.38 inference(negated_conjecture,[],[f4])).
% 0.14/0.38 thf(f4,conjecture,(
% 0.14/0.38 uniqinunit => (secondinupair => (setukpairinjR12 => ! [X1,X0,X3,X2] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X2 = X3) => (X1 = X3)))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1)).
% 0.14/0.38 thf(f76,plain,(
% 0.14/0.38 (sK6 = sK7)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f75])).
% 0.14/0.38 thf(f75,plain,(
% 0.14/0.38 ($true != $true) | (sK6 = sK7)),
% 0.14/0.38 inference(superposition,[],[f58,f73])).
% 0.14/0.38 thf(f73,plain,(
% 0.14/0.38 ($true = (in @ sK6 @ (setadjoin @ sK7 @ emptyset)))),
% 0.14/0.38 inference(superposition,[],[f59,f69])).
% 0.14/0.38 thf(f69,plain,(
% 0.14/0.38 ((setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) = (setadjoin @ sK7 @ emptyset))),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f68])).
% 0.14/0.38 thf(f68,plain,(
% 0.14/0.38 ((setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) = (setadjoin @ sK7 @ emptyset)) | ($true != $true)),
% 0.14/0.38 inference(superposition,[],[f58,f64])).
% 0.14/0.38 thf(f64,plain,(
% 0.14/0.38 ((in @ (setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) @ (setadjoin @ (setadjoin @ sK7 @ emptyset) @ emptyset)) = $true)),
% 0.14/0.38 inference(forward_demodulation,[],[f63,f57])).
% 0.14/0.38 thf(f57,plain,(
% 0.14/0.38 ( ! [X3 : $i] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset))) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f56])).
% 0.14/0.38 thf(f56,plain,(
% 0.14/0.38 ( ! [X3 : $i] : (($true != $true) | ((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset))) )),
% 0.14/0.38 inference(equality_resolution,[],[f49])).
% 0.14/0.38 thf(f49,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) | (X2 != X3) | ($true != $true)) )),
% 0.14/0.38 inference(definition_unfolding,[],[f33,f45])).
% 0.14/0.38 thf(f45,plain,(
% 0.14/0.38 (setukpairinjR12 = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f32])).
% 0.14/0.38 thf(f33,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) | (X2 != X3) | (setukpairinjR12 != $true)) )),
% 0.14/0.38 inference(cnf_transformation,[],[f21])).
% 0.14/0.38 thf(f21,plain,(
% 0.14/0.38 ((setukpairinjR12 = $true) | (((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset)) & (sK1 = sK0))) & (! [X2,X3] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) | (X2 != X3)) | (setukpairinjR12 != $true))),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f20])).
% 0.14/0.38 thf(f20,plain,(
% 0.14/0.38 ? [X0,X1] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset)) & (X0 = X1)) => (((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ emptyset)) & (sK1 = sK0))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f19,plain,(
% 0.14/0.38 ((setukpairinjR12 = $true) | ? [X0,X1] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset)) & (X0 = X1))) & (! [X2,X3] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) | (X2 != X3)) | (setukpairinjR12 != $true))),
% 0.14/0.38 inference(rectify,[],[f18])).
% 0.14/0.38 thf(f18,plain,(
% 0.14/0.38 ((setukpairinjR12 = $true) | ? [X1,X0] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)) & (X0 = X1))) & (! [X1,X0] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)) | (X0 != X1)) | (setukpairinjR12 != $true))),
% 0.14/0.38 inference(nnf_transformation,[],[f15])).
% 0.14/0.38 thf(f15,plain,(
% 0.14/0.38 (setukpairinjR12 = $true) <=> ! [X1,X0] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)) | (X0 != X1))),
% 0.14/0.38 inference(ennf_transformation,[],[f13])).
% 0.14/0.38 thf(f13,plain,(
% 0.14/0.38 (setukpairinjR12 = $true) <=> ! [X1,X0] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)))),
% 0.14/0.38 inference(fool_elimination,[],[f3])).
% 0.14/0.38 thf(f3,axiom,(
% 0.14/0.38 (! [X0,X1] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) = setukpairinjR12)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12)).
% 0.14/0.38 thf(f63,plain,(
% 0.14/0.38 ((in @ (setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) @ (setadjoin @ (setadjoin @ sK7 @ emptyset) @ (setadjoin @ (setadjoin @ sK7 @ (setadjoin @ sK7 @ emptyset)) @ emptyset))) = $true)),
% 0.14/0.38 inference(superposition,[],[f59,f55])).
% 0.14/0.38 thf(f55,plain,(
% 0.14/0.38 ((setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK7 @ emptyset) @ (setadjoin @ (setadjoin @ sK7 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)))),
% 0.14/0.38 inference(definition_unfolding,[],[f43,f41,f41])).
% 0.14/0.38 thf(f41,plain,(
% 0.14/0.38 (sK9 = sK7)),
% 0.14/0.38 inference(cnf_transformation,[],[f32])).
% 0.14/0.38 thf(f43,plain,(
% 0.14/0.38 ((setadjoin @ (setadjoin @ sK9 @ emptyset) @ (setadjoin @ (setadjoin @ sK9 @ (setadjoin @ sK7 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK6 @ emptyset)) @ emptyset)))),
% 0.14/0.38 inference(cnf_transformation,[],[f32])).
% 0.14/0.38 thf(f59,plain,(
% 0.14/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f50])).
% 0.14/0.38 thf(f50,plain,(
% 0.14/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | ($true != $true)) )),
% 0.14/0.38 inference(definition_unfolding,[],[f37,f44])).
% 0.14/0.38 thf(f44,plain,(
% 0.14/0.38 (secondinupair = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f32])).
% 0.14/0.38 thf(f37,plain,(
% 0.14/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (secondinupair != $true)) )),
% 0.14/0.38 inference(cnf_transformation,[],[f25])).
% 0.14/0.38 thf(f25,plain,(
% 0.14/0.38 (! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (secondinupair != $true)) & ((secondinupair = $true) | ($true != (in @ sK2 @ (setadjoin @ sK3 @ (setadjoin @ sK2 @ emptyset)))))),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f23,f24])).
% 0.14/0.38 thf(f24,plain,(
% 0.14/0.38 ? [X2,X3] : ((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))) != $true) => ($true != (in @ sK2 @ (setadjoin @ sK3 @ (setadjoin @ sK2 @ emptyset))))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f23,plain,(
% 0.14/0.38 (! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (secondinupair != $true)) & ((secondinupair = $true) | ? [X2,X3] : ((in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset))) != $true))),
% 0.14/0.38 inference(rectify,[],[f22])).
% 0.14/0.38 thf(f22,plain,(
% 0.14/0.38 (! [X1,X0] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) | (secondinupair != $true)) & ((secondinupair = $true) | ? [X1,X0] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true))),
% 0.14/0.38 inference(nnf_transformation,[],[f8])).
% 0.14/0.38 thf(f8,plain,(
% 0.14/0.38 ! [X1,X0] : ((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) <=> (secondinupair = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f7])).
% 0.14/0.38 thf(f7,plain,(
% 0.14/0.38 (! [X0,X1] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 0.14/0.38 inference(rectify,[],[f2])).
% 0.14/0.38 thf(f2,axiom,(
% 0.14/0.38 (! [X0,X1] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair)).
% 0.14/0.38 thf(f58,plain,(
% 0.14/0.38 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f52])).
% 0.14/0.38 thf(f52,plain,(
% 0.14/0.38 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | ($true != $true)) )),
% 0.14/0.38 inference(definition_unfolding,[],[f40,f46])).
% 0.14/0.38 thf(f46,plain,(
% 0.14/0.38 (uniqinunit = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f32])).
% 0.14/0.38 thf(f40,plain,(
% 0.14/0.38 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (uniqinunit != $true)) )),
% 0.14/0.38 inference(cnf_transformation,[],[f29])).
% 0.14/0.38 thf(f29,plain,(
% 0.14/0.38 (! [X0,X1] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset)))) | (uniqinunit != $true)) & ((uniqinunit = $true) | ((sK4 != sK5) & ((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) = $true)))),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f27,f28])).
% 0.14/0.38 thf(f28,plain,(
% 0.14/0.38 ? [X2,X3] : ((X2 != X3) & ((in @ X3 @ (setadjoin @ X2 @ emptyset)) = $true)) => ((sK4 != sK5) & ((in @ sK5 @ (setadjoin @ sK4 @ emptyset)) = $true))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f27,plain,(
% 0.14/0.38 (! [X0,X1] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset)))) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2,X3] : ((X2 != X3) & ((in @ X3 @ (setadjoin @ X2 @ emptyset)) = $true)))),
% 0.14/0.38 inference(rectify,[],[f26])).
% 0.14/0.38 thf(f26,plain,(
% 0.14/0.38 (! [X1,X0] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X1,X0] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)))),
% 0.14/0.38 inference(nnf_transformation,[],[f14])).
% 0.14/0.38 thf(f14,plain,(
% 0.14/0.38 ! [X1,X0] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) <=> (uniqinunit = $true)),
% 0.14/0.38 inference(ennf_transformation,[],[f10])).
% 0.14/0.38 thf(f10,plain,(
% 0.14/0.38 ! [X0,X1] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f9])).
% 0.14/0.38 thf(f9,plain,(
% 0.14/0.38 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.14/0.38 inference(rectify,[],[f1])).
% 0.14/0.38 thf(f1,axiom,(
% 0.14/0.38 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (11940)------------------------------
% 0.14/0.38 % (11940)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (11940)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (11940)Memory used [KB]: 5500
% 0.14/0.38 % (11940)Time elapsed: 0.010 s
% 0.14/0.38 % (11940)Instructions burned: 9 (million)
% 0.14/0.38 % (11940)------------------------------
% 0.14/0.38 % (11940)------------------------------
% 0.14/0.38 % (11934)Success in time 0.012 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------