TSTP Solution File: SEU673^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU673^2 : 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 : n005.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 03:50:30 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU673^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.14 % 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 : n005.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
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:13:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.14/0.38 % (22659)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (22657)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)
% 0.14/0.38 % (22658)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)
% 0.14/0.38 % (22656)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (22661)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)
% 0.14/0.38 % (22662)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (22663)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)
% 0.14/0.38 % (22659)Instruction limit reached!
% 0.14/0.38 % (22659)------------------------------
% 0.14/0.38 % (22659)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22659)Termination reason: Unknown
% 0.14/0.38 % (22659)Termination phase: Preprocessing 3
% 0.14/0.38
% 0.14/0.38 % (22659)Memory used [KB]: 1023
% 0.14/0.38 % (22659)Time elapsed: 0.004 s
% 0.14/0.38 % (22659)Instructions burned: 3 (million)
% 0.14/0.38 % (22659)------------------------------
% 0.14/0.38 % (22659)------------------------------
% 0.14/0.38 % (22663)Instruction limit reached!
% 0.14/0.38 % (22663)------------------------------
% 0.14/0.38 % (22663)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22663)Termination reason: Unknown
% 0.14/0.38 % (22663)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (22663)Memory used [KB]: 1023
% 0.14/0.38 % (22663)Time elapsed: 0.004 s
% 0.14/0.38 % (22663)Instructions burned: 3 (million)
% 0.14/0.38 % (22663)------------------------------
% 0.14/0.38 % (22663)------------------------------
% 0.14/0.38 % (22657)Instruction limit reached!
% 0.14/0.38 % (22657)------------------------------
% 0.14/0.38 % (22657)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22657)Termination reason: Unknown
% 0.14/0.38 % (22657)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (22657)Memory used [KB]: 1023
% 0.14/0.38 % (22657)Time elapsed: 0.004 s
% 0.14/0.38 % (22657)Instructions burned: 5 (million)
% 0.14/0.38 % (22657)------------------------------
% 0.14/0.38 % (22657)------------------------------
% 0.14/0.38 % (22660)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)
% 0.14/0.38 % (22660)Instruction limit reached!
% 0.14/0.38 % (22660)------------------------------
% 0.14/0.38 % (22660)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22660)Termination reason: Unknown
% 0.14/0.38 % (22660)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (22660)Memory used [KB]: 895
% 0.14/0.38 % (22660)Time elapsed: 0.003 s
% 0.14/0.38 % (22660)Instructions burned: 2 (million)
% 0.14/0.38 % (22660)------------------------------
% 0.14/0.38 % (22660)------------------------------
% 0.14/0.38 % (22661)First to succeed.
% 0.14/0.39 % (22661)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% 0.14/0.39 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.14/0.39 thf(func_def_3, type, setunion: $i > $i).
% 0.14/0.39 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.14/0.39 thf(func_def_7, type, subset: $i > $i > $o).
% 0.14/0.39 thf(func_def_8, type, kpair: $i > $i > $i).
% 0.14/0.39 thf(func_def_9, type, cartprod: $i > $i > $i).
% 0.14/0.39 thf(func_def_10, type, singleton: $i > $o).
% 0.14/0.39 thf(func_def_11, type, ex1: $i > ($i > $o) > $o).
% 0.14/0.39 thf(func_def_13, type, breln: $i > $i > $i > $o).
% 0.14/0.39 thf(func_def_14, type, func: $i > $i > $i > $o).
% 0.14/0.39 thf(func_def_38, type, sK10: $i > $o).
% 0.14/0.39 thf(func_def_42, type, ph13: !>[X0: $tType]:(X0)).
% 0.14/0.39 thf(f87,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(subsumption_resolution,[],[f86,f48])).
% 0.14/0.39 thf(f48,plain,(
% 0.14/0.39 ((in @ sK3 @ sK2) = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f33])).
% 0.14/0.39 thf(f33,plain,(
% 0.14/0.39 (funcImageSingleton = $true) & (dsetconstrEL = $true) & (($true = (func @ sK2 @ sK0 @ sK1)) & (((in @ (setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1)))) @ sK0) != $true) & ((in @ sK3 @ sK2) = $true))) & (theprop = $true)),
% 0.14/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f29,f32,f31])).
% 0.14/0.39 thf(f31,plain,(
% 0.14/0.39 ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (((in @ (setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) @ X0) != $true) & ((in @ X3 @ X2) = $true))) => (($true = (func @ sK2 @ sK0 @ sK1)) & ? [X3] : (((in @ (setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK1)))) @ sK0) != $true) & ((in @ X3 @ sK2) = $true)))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f32,plain,(
% 0.14/0.39 ? [X3] : (((in @ (setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK1)))) @ sK0) != $true) & ((in @ X3 @ sK2) = $true)) => (((in @ (setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1)))) @ sK0) != $true) & ((in @ sK3 @ sK2) = $true))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f29,plain,(
% 0.14/0.39 (funcImageSingleton = $true) & (dsetconstrEL = $true) & ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (((in @ (setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) @ X0) != $true) & ((in @ X3 @ X2) = $true))) & (theprop = $true)),
% 0.14/0.39 inference(flattening,[],[f28])).
% 0.14/0.39 thf(f28,plain,(
% 0.14/0.39 ((? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (((in @ (setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) @ X0) != $true) & ((in @ X3 @ X2) = $true))) & (funcImageSingleton = $true)) & (theprop = $true)) & (dsetconstrEL = $true)),
% 0.14/0.39 inference(ennf_transformation,[],[f16])).
% 0.14/0.39 thf(f16,plain,(
% 0.14/0.39 ~((dsetconstrEL = $true) => ((theprop = $true) => ((funcImageSingleton = $true) => ! [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) => ! [X3] : (((in @ X3 @ X2) = $true) => ((in @ (setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) @ X0) = $true))))))),
% 0.14/0.39 inference(fool_elimination,[],[f15])).
% 0.14/0.39 thf(f15,plain,(
% 0.14/0.39 ~(dsetconstrEL => (theprop => (funcImageSingleton => ! [X0,X1,X2] : ((func @ X2 @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (in @ (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X1)))) @ X0))))))),
% 0.14/0.39 inference(rectify,[],[f9])).
% 0.14/0.39 thf(f9,negated_conjecture,(
% 0.14/0.39 ~(dsetconstrEL => (theprop => (funcImageSingleton => ! [X5,X8,X0] : ((func @ X0 @ X5 @ X8) => ! [X2] : ((in @ X2 @ X0) => (in @ (setunion @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8)))) @ X5))))))),
% 0.14/0.39 inference(negated_conjecture,[],[f8])).
% 0.14/0.39 thf(f8,conjecture,(
% 0.14/0.39 dsetconstrEL => (theprop => (funcImageSingleton => ! [X5,X8,X0] : ((func @ X0 @ X5 @ X8) => ! [X2] : ((in @ X2 @ X0) => (in @ (setunion @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8)))) @ X5)))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp)).
% 0.14/0.39 thf(f86,plain,(
% 0.14/0.39 ((in @ sK3 @ sK2) != $true)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f85])).
% 0.14/0.39 thf(f85,plain,(
% 0.14/0.39 ($true != $true) | ((in @ sK3 @ sK2) != $true)),
% 0.14/0.39 inference(superposition,[],[f84,f50])).
% 0.14/0.39 thf(f50,plain,(
% 0.14/0.39 ($true = (func @ sK2 @ sK0 @ sK1))),
% 0.14/0.39 inference(cnf_transformation,[],[f33])).
% 0.14/0.39 thf(f84,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (($true != (func @ X0 @ sK0 @ sK1)) | ((in @ sK3 @ X0) != $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f83])).
% 0.14/0.39 thf(f83,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (($true != (func @ X0 @ sK0 @ sK1)) | ($true != $true) | ((in @ sK3 @ X0) != $true)) )),
% 0.14/0.39 inference(superposition,[],[f82,f73])).
% 0.14/0.39 thf(f73,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true) | ($true != (func @ X2 @ X0 @ X1))) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f66])).
% 0.14/0.39 thf(f66,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true) | ($true != (func @ X2 @ X0 @ X1)) | ($true != $true)) )),
% 0.14/0.39 inference(definition_unfolding,[],[f59,f52])).
% 0.14/0.39 thf(f52,plain,(
% 0.14/0.39 (funcImageSingleton = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f33])).
% 0.14/0.39 thf(f59,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true) | ($true != (func @ X2 @ X0 @ X1)) | (funcImageSingleton != $true)) )),
% 0.14/0.39 inference(cnf_transformation,[],[f42])).
% 0.14/0.39 thf(f42,plain,(
% 0.14/0.39 (! [X0,X1,X2] : (! [X3] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (func @ X2 @ X0 @ X1))) | (funcImageSingleton != $true)) & ((funcImageSingleton = $true) | ((((singleton @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK8 @ Y0) @ sK6)))) != $true) & ((in @ sK8 @ sK7) = $true)) & ((func @ sK7 @ sK5 @ sK6) = $true)))),
% 0.14/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f39,f41,f40])).
% 0.14/0.39 thf(f40,plain,(
% 0.14/0.39 ? [X4,X5,X6] : (? [X7] : (((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X5)))) != $true) & ((in @ X7 @ X6) = $true)) & ((func @ X6 @ X4 @ X5) = $true)) => (? [X7] : (((singleton @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ sK6)))) != $true) & ((in @ X7 @ sK7) = $true)) & ((func @ sK7 @ sK5 @ sK6) = $true))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f41,plain,(
% 0.14/0.39 ? [X7] : (((singleton @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ sK6)))) != $true) & ((in @ X7 @ sK7) = $true)) => (((singleton @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK8 @ Y0) @ sK6)))) != $true) & ((in @ sK8 @ sK7) = $true))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f39,plain,(
% 0.14/0.39 (! [X0,X1,X2] : (! [X3] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (func @ X2 @ X0 @ X1))) | (funcImageSingleton != $true)) & ((funcImageSingleton = $true) | ? [X4,X5,X6] : (? [X7] : (((singleton @ (dsetconstr @ X4 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X5)))) != $true) & ((in @ X7 @ X6) = $true)) & ((func @ X6 @ X4 @ X5) = $true)))),
% 0.14/0.39 inference(rectify,[],[f38])).
% 0.14/0.39 thf(f38,plain,(
% 0.14/0.39 (! [X0,X1,X2] : (! [X3] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (func @ X2 @ X0 @ X1))) | (funcImageSingleton != $true)) & ((funcImageSingleton = $true) | ? [X0,X1,X2] : (? [X3] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) != $true) & ((in @ X3 @ X2) = $true)) & ($true = (func @ X2 @ X0 @ X1))))),
% 0.14/0.39 inference(nnf_transformation,[],[f30])).
% 0.14/0.39 thf(f30,plain,(
% 0.14/0.39 ! [X0,X1,X2] : (! [X3] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true) | ((in @ X3 @ X2) != $true)) | ($true != (func @ X2 @ X0 @ X1))) <=> (funcImageSingleton = $true)),
% 0.14/0.39 inference(ennf_transformation,[],[f12])).
% 0.14/0.39 thf(f12,plain,(
% 0.14/0.39 (funcImageSingleton = $true) <=> ! [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) => ! [X3] : (((in @ X3 @ X2) = $true) => ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X1)))) = $true)))),
% 0.14/0.39 inference(fool_elimination,[],[f11])).
% 0.14/0.39 thf(f11,plain,(
% 0.14/0.39 (funcImageSingleton = ! [X0,X1,X2] : ((func @ X2 @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X1)))))))),
% 0.14/0.39 inference(rectify,[],[f7])).
% 0.14/0.39 thf(f7,axiom,(
% 0.14/0.39 (funcImageSingleton = ! [X5,X8,X0] : ((func @ X0 @ X5 @ X8) => ! [X2] : ((in @ X2 @ X0) => (singleton @ (dsetconstr @ X5 @ (^[X3 : $i] : (in @ (kpair @ X2 @ X3) @ X8)))))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton)).
% 0.14/0.39 thf(f82,plain,(
% 0.14/0.39 ($true != (singleton @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1)))))),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f81])).
% 0.14/0.39 thf(f81,plain,(
% 0.14/0.39 ($true != (singleton @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1))))) | ($true != $true)),
% 0.14/0.39 inference(superposition,[],[f49,f78])).
% 0.14/0.39 thf(f78,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i > $o] : (((in @ (setunion @ (dsetconstr @ X0 @ X1)) @ X0) = $true) | ($true != (singleton @ (dsetconstr @ X0 @ X1)))) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f77])).
% 0.14/0.39 thf(f77,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i > $o] : (($true != $true) | ($true != (singleton @ (dsetconstr @ X0 @ X1))) | ((in @ (setunion @ (dsetconstr @ X0 @ X1)) @ X0) = $true)) )),
% 0.14/0.39 inference(superposition,[],[f75,f76])).
% 0.14/0.39 thf(f76,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ((singleton @ X1) != $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f65])).
% 0.14/0.39 thf(f65,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((in @ (setunion @ X1) @ X1) = $true) | ($true != $true) | ((singleton @ X1) != $true)) )),
% 0.14/0.39 inference(definition_unfolding,[],[f53,f47])).
% 0.14/0.39 thf(f47,plain,(
% 0.14/0.39 (theprop = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f33])).
% 0.14/0.39 thf(f53,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true) | (theprop != $true)) )),
% 0.14/0.39 inference(cnf_transformation,[],[f37])).
% 0.14/0.39 thf(f37,plain,(
% 0.14/0.39 ((theprop = $true) | (((singleton @ sK4) = $true) & ((in @ (setunion @ sK4) @ sK4) != $true))) & (! [X1] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true)) | (theprop != $true))),
% 0.14/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f35,f36])).
% 0.14/0.39 thf(f36,plain,(
% 0.14/0.39 ? [X0] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true)) => (((singleton @ sK4) = $true) & ((in @ (setunion @ sK4) @ sK4) != $true))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f35,plain,(
% 0.14/0.39 ((theprop = $true) | ? [X0] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true))) & (! [X1] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true)) | (theprop != $true))),
% 0.14/0.39 inference(rectify,[],[f34])).
% 0.14/0.39 thf(f34,plain,(
% 0.14/0.39 ((theprop = $true) | ? [X0] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true))) & (! [X0] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) | (theprop != $true))),
% 0.14/0.39 inference(nnf_transformation,[],[f26])).
% 0.14/0.39 thf(f26,plain,(
% 0.14/0.39 (theprop = $true) <=> ! [X0] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true))),
% 0.14/0.39 inference(ennf_transformation,[],[f23])).
% 0.14/0.39 thf(f23,plain,(
% 0.14/0.39 (theprop = $true) <=> ! [X0] : (((singleton @ X0) = $true) => ((in @ (setunion @ X0) @ X0) = $true))),
% 0.14/0.39 inference(fool_elimination,[],[f22])).
% 0.14/0.39 thf(f22,plain,(
% 0.14/0.39 (! [X0] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 0.14/0.39 inference(rectify,[],[f4])).
% 0.14/0.39 thf(f4,axiom,(
% 0.14/0.39 (! [X4] : ((singleton @ X4) => (in @ (setunion @ X4) @ X4)) = theprop)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop)).
% 0.14/0.39 thf(f75,plain,(
% 0.14/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X0 @ X1)) != $true) | ((in @ X2 @ X0) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f74])).
% 0.14/0.39 thf(f74,plain,(
% 0.14/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f70])).
% 0.14/0.39 thf(f70,plain,(
% 0.14/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != $true) | ((in @ X2 @ X0) = $true) | ((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true)) )),
% 0.14/0.39 inference(definition_unfolding,[],[f62,f51])).
% 0.14/0.39 thf(f51,plain,(
% 0.14/0.39 (dsetconstrEL = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f33])).
% 0.14/0.39 thf(f62,plain,(
% 0.14/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true) | (dsetconstrEL != $true)) )),
% 0.14/0.39 inference(cnf_transformation,[],[f46])).
% 0.14/0.39 thf(f46,plain,(
% 0.14/0.39 (! [X0,X1 : $i > $o,X2] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | (((in @ sK11 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: (sK10 @ Y0)))) = $true) & ($true != (in @ sK11 @ sK9))))),
% 0.14/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f44,f45])).
% 0.14/0.39 thf(f45,plain,(
% 0.14/0.39 ? [X3,X4 : $i > $o,X5] : (((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true) & ((in @ X5 @ X3) != $true)) => (((in @ sK11 @ (dsetconstr @ sK9 @ (^[Y0 : $i]: (sK10 @ Y0)))) = $true) & ($true != (in @ sK11 @ sK9)))),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f44,plain,(
% 0.14/0.39 (! [X0,X1 : $i > $o,X2] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X3,X4 : $i > $o,X5] : (((in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))) = $true) & ((in @ X5 @ X3) != $true)))),
% 0.14/0.39 inference(rectify,[],[f43])).
% 0.14/0.39 thf(f43,plain,(
% 0.14/0.39 (! [X0,X1 : $i > $o,X2] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true)) | (dsetconstrEL != $true)) & ((dsetconstrEL = $true) | ? [X0,X1 : $i > $o,X2] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) & ((in @ X2 @ X0) != $true)))),
% 0.14/0.39 inference(nnf_transformation,[],[f27])).
% 0.14/0.39 thf(f27,plain,(
% 0.14/0.39 ! [X0,X1 : $i > $o,X2] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) | ((in @ X2 @ X0) = $true)) <=> (dsetconstrEL = $true)),
% 0.14/0.39 inference(ennf_transformation,[],[f14])).
% 0.14/0.39 thf(f14,plain,(
% 0.14/0.39 (dsetconstrEL = $true) <=> ! [X0,X1 : $i > $o,X2] : (((in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) => ((in @ X2 @ X0) = $true))),
% 0.14/0.39 inference(fool_elimination,[],[f13])).
% 0.14/0.39 thf(f13,plain,(
% 0.14/0.39 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 0.14/0.39 inference(rectify,[],[f1])).
% 0.14/0.39 thf(f1,axiom,(
% 0.14/0.39 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X2 @ X0)) = dsetconstrEL)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)).
% 0.14/0.39 thf(f49,plain,(
% 0.14/0.39 ((in @ (setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK1)))) @ sK0) != $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f33])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (22661)------------------------------
% 0.14/0.39 % (22661)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (22661)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (22661)Memory used [KB]: 5500
% 0.14/0.39 % (22661)Time elapsed: 0.010 s
% 0.14/0.39 % (22661)Instructions burned: 7 (million)
% 0.14/0.39 % (22661)------------------------------
% 0.14/0.39 % (22661)------------------------------
% 0.14/0.39 % (22654)Success in time 0.012 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------