%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO173^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:49:05 AM UTC 2026
% Result : Theorem 1.10s 0.45s
% Output : Refutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO173^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.16 % Computer : n026.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:39:43 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 Running first-order model finding
% 0.09/0.19 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/0.45 % (837451)Will run a generic schedule for satisfiability detection.
% 1.10/0.45 % (837458)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3729351311:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.10/0.45 % (837457)% WARNING: option uhcvi not known.
% 1.10/0.45 % (837456)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2551336497_2999 on theBenchmark for (2999ds/0Mi)
% 1.10/0.45 % (837459)dis+10_1_sil=32000:sp=arity:random_seed=809275061:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.10/0.45 % (837460)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2331480906:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.10/0.45 % (837461)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4072923089:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.10/0.45 % (837462)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1313143671:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.10/0.45 % Exception at run slice level
% 1.10/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.45 % (837460)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.45 % (837457)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=335498372:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.10/0.45 % (837457)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.45 % (837457)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.10/0.45 % (837469)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2996252967:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.10/0.45 % Exception at run slice level
% 1.10/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.45 % (837472)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=535637956:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.10/0.45 % (837459)Instruction limit reached!
% 1.10/0.45 % (837459)------------------------------
% 1.10/0.45 % (837459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837459)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837459)Termination reason: Instruction limit
% 1.10/0.45 % (837459)Termination phase: Saturation
% 1.10/0.45 % (837459)Time elapsed: 0.054 s
% 1.10/0.45 % (837459)Peak memory usage: 12 MB
% 1.10/0.45 % (837459)Instructions burned: 105 (million)
% 1.10/0.45 % (837460)Instruction limit reached!
% 1.10/0.45 % (837460)------------------------------
% 1.10/0.45 % (837460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837460)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837460)Termination reason: Instruction limit
% 1.10/0.45 % (837460)Termination phase: Saturation
% 1.10/0.45 % (837460)Time elapsed: 0.058 s
% 1.10/0.45 % (837460)Peak memory usage: 12 MB
% 1.10/0.45 % (837460)Instructions burned: 116 (million)
% 1.10/0.45 % (837461)Instruction limit reached!
% 1.10/0.45 % (837461)------------------------------
% 1.10/0.45 % (837461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837461)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837461)Termination reason: Instruction limit
% 1.10/0.45 % (837461)Termination phase: Saturation
% 1.10/0.45 % (837461)Time elapsed: 0.068 s
% 1.10/0.45 % (837461)Peak memory usage: 12 MB
% 1.10/0.45 % (837461)Instructions burned: 133 (million)
% 1.10/0.45 % (837474)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3538183038:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.10/0.45 % (837474)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.45 % (837474)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.10/0.45 % (837475)ott-21_1_sil=16000:fs=off:random_seed=3387646526:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.10/0.45 % (837462)Instruction limit reached!
% 1.10/0.45 % (837462)------------------------------
% 1.10/0.45 % (837462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837462)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837462)Termination reason: Instruction limit
% 1.10/0.45 % (837462)Termination phase: Saturation
% 1.10/0.45 % (837462)Time elapsed: 0.082 s
% 1.10/0.45 % (837462)Peak memory usage: 12 MB
% 1.10/0.45 % (837462)Instructions burned: 160 (million)
% 1.10/0.45 % (837476)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1173101178:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.10/0.45 % (837479)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3747588982:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.10/0.45 % Exception at run slice level
% 1.10/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.45 % (837472)Instruction limit reached!
% 1.10/0.45 % (837472)------------------------------
% 1.10/0.45 % (837472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837472)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837472)Termination reason: Instruction limit
% 1.10/0.45 % (837472)Termination phase: Saturation
% 1.10/0.45 % (837472)Time elapsed: 0.070 s
% 1.10/0.45 % (837472)Peak memory usage: 12 MB
% 1.10/0.45 % (837472)Instructions burned: 132 (million)
% 1.10/0.45 % (837482)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3885257077:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.10/0.45 % (837483)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1769543384:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.10/0.45 % Exception at run slice level
% 1.10/0.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.10/0.45 % (837486)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=508197961:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.10/0.45 % (837486)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.45 % (837475)Instruction limit reached!
% 1.10/0.45 % (837475)------------------------------
% 1.10/0.45 % (837475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837475)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837475)Termination reason: Instruction limit
% 1.10/0.45 % (837475)Termination phase: Saturation
% 1.10/0.45 % (837475)Time elapsed: 0.080 s
% 1.10/0.45 % (837475)Peak memory usage: 12 MB
% 1.10/0.45 % (837475)Instructions burned: 181 (million)
% 1.10/0.45 % (837488)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=792869793:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.10/0.45 % (837488)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.10/0.45 % (837458) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-837451-837458"...
% 1.10/0.45 % (837458)...printing done.
% 1.10/0.45 % (837458)Refutation found. Thanks to Tanya!
% 1.10/0.45 % SZS status Theorem for theBenchmark
% 1.10/0.45 % SZS output start Proof for theBenchmark
% 1.10/0.45 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.10/0.45 thf(func_def_0, type, nt: ($i > $i)).
% 1.10/0.45 thf(func_def_1, type, imp: ($i > $i > $i)).
% 1.10/0.45 thf(func_def_2, type, cT: ($i > $o)).
% 1.10/0.45 thf(f1,conjecture,(
% 1.10/0.45 ~(? [X3 : $i] : ~(cT @ (imp @ (nt @ (nt @ X3)) @ X3)) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ (nt @ X0) @ (nt @ X1)) @ (imp @ X1 @ X0))) & ! [X0 : $i,X1 : $i,X2 : $i] : (cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X2)) @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ X0 @ (imp @ X1 @ X0))) & ! [X0 : $i,X1 : $i] : ((cT @ X1) | ~(cT @ X0) | ~(cT @ (imp @ X0 @ X1))))),
% 1.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cLCL077_1)).
% 1.10/0.45 thf(f2,negated_conjecture,(
% 1.10/0.45 ~ ~(? [X3 : $i] : ~(cT @ (imp @ (nt @ (nt @ X3)) @ X3)) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ (nt @ X0) @ (nt @ X1)) @ (imp @ X1 @ X0))) & ! [X0 : $i,X1 : $i,X2 : $i] : (cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X2)) @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ X0 @ (imp @ X1 @ X0))) & ! [X0 : $i,X1 : $i] : ((cT @ X1) | ~(cT @ X0) | ~(cT @ (imp @ X0 @ X1))))),
% 1.10/0.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.10/0.45 thf(f3,plain,(
% 1.10/0.45 ~ ~(? [X0 : $i] : ~(cT @ (imp @ (nt @ (nt @ X0)) @ X0)) & ! [X1 : $i,X2 : $i] : (cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X2)) @ (imp @ X2 @ X1))) & ! [X3 : $i,X4 : $i,X5 : $i] : (cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X5)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X5)))) & ! [X6 : $i,X7 : $i] : (cT @ (imp @ X6 @ (imp @ X7 @ X6))) & ! [X8 : $i,X9 : $i] : ((cT @ X9) | ~(cT @ X8) | ~(cT @ (imp @ X8 @ X9))))),
% 1.10/0.45 inference(rectify,[],[f2])).
% 1.10/0.45 thf(f4,plain,(
% 1.10/0.45 ~ ~(? [X0 : $i] : ~ (((cT @ (imp @ (nt @ (nt @ X0)) @ X0))) = $true) & ! [X1 : $i,X2 : $i] : (((cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X2)) @ (imp @ X2 @ X1)))) = $true) & ! [X3 : $i,X4 : $i,X5 : $i] : (((cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X5)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X5))))) = $true) & ! [X6 : $i,X7 : $i] : (((cT @ (imp @ X6 @ (imp @ X7 @ X6)))) = $true) & ! [X8 : $i,X9 : $i] : ((((cT @ X9)) = $true) | ~ (((cT @ X8)) = $true) | ~ (((cT @ (imp @ X8 @ X9))) = $true)))),
% 1.10/0.45 inference(fool_elimination,[],[f3])).
% 1.10/0.45 thf(f5,plain,(
% 1.10/0.45 ? [X0 : $i] : (((cT @ (imp @ (nt @ (nt @ X0)) @ X0))) != $true) & ! [X1 : $i,X2 : $i] : (((cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X2)) @ (imp @ X2 @ X1)))) = $true) & ! [X3 : $i,X4 : $i,X5 : $i] : (((cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X5)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X5))))) = $true) & ! [X6 : $i,X7 : $i] : (((cT @ (imp @ X6 @ (imp @ X7 @ X6)))) = $true) & ! [X8 : $i,X9 : $i] : ((((cT @ X9)) = $true) | (((cT @ X8)) != $true) | (((cT @ (imp @ X8 @ X9))) != $true))),
% 1.10/0.45 inference(flattening,[],[f4])).
% 1.10/0.45 thf(f6,plain,(
% 1.10/0.45 ($true != ((cT @ (imp @ (nt @ (nt @ sK0)) @ sK0)))) & ! [X1 : $i,X2 : $i] : (((cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X2)) @ (imp @ X2 @ X1)))) = $true) & ! [X3 : $i,X4 : $i,X5 : $i] : (((cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X5)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X5))))) = $true) & ! [X6 : $i,X7 : $i] : (((cT @ (imp @ X6 @ (imp @ X7 @ X6)))) = $true) & ! [X8 : $i,X9 : $i] : ((((cT @ X9)) = $true) | (((cT @ X8)) != $true) | (((cT @ (imp @ X8 @ X9))) != $true))),
% 1.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f5])).
% 1.10/0.45 thf(f7,plain,(
% 1.10/0.45 ( ! [X8 : $i,X9 : $i] : ((((cT @ (imp @ X8 @ X9))) != $true) | (((cT @ X8)) != $true) | (((cT @ X9)) = $true)) )),
% 1.10/0.45 inference(cnf_transformation,[],[f6])).
% 1.10/0.45 thf(f8,plain,(
% 1.10/0.45 ( ! [X6 : $i,X7 : $i] : ((((cT @ (imp @ X6 @ (imp @ X7 @ X6)))) = $true)) )),
% 1.10/0.45 inference(cnf_transformation,[],[f6])).
% 1.10/0.45 thf(f9,plain,(
% 1.10/0.45 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X5)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X5))))) = $true)) )),
% 1.10/0.45 inference(cnf_transformation,[],[f6])).
% 1.10/0.45 thf(f10,plain,(
% 1.10/0.45 ( ! [X2 : $i,X1 : $i] : ((((cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X2)) @ (imp @ X2 @ X1)))) = $true)) )),
% 1.10/0.45 inference(cnf_transformation,[],[f6])).
% 1.10/0.45 thf(f11,plain,(
% 1.10/0.45 ($true != ((cT @ (imp @ (nt @ (nt @ sK0)) @ sK0))))),
% 1.10/0.45 inference(cnf_transformation,[],[f6])).
% 1.10/0.45 thf(f13,definition,(
% 1.10/0.45 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.10/0.45 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.10/0.45 thf(f23,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cT @ X0)) != $true) | ($true = ((cT @ (imp @ X1 @ X0))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f7,f8])).
% 1.10/0.45 thf(f24,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : ((((cT @ X0)) != $true) | ($true = ((cT @ (imp @ X1 @ X0))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f23])).
% 1.10/0.45 thf(f39,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ (imp @ X2 @ (imp @ X0 @ (imp @ X1 @ X0))))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f24,f8])).
% 1.10/0.45 thf(f40,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ X2 @ (imp @ X0 @ (imp @ X1 @ X0))))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f39])).
% 1.10/0.45 thf(f82,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cT @ X0)) != $true) | (((cT @ X1)) = $true) | (((cT @ (imp @ X0 @ X1))) = $false)) )),
% 1.10/0.45 inference(constrained_superposition,[],[f7,f13])).
% 1.10/0.45 thf(f83,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ (imp @ X1 @ X0)))) | (((cT @ X0)) = $false)) )),
% 1.10/0.45 inference(constrained_superposition,[],[f24,f13])).
% 1.10/0.45 thf(f85,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ X1 @ X0)))) | (((cT @ X0)) = $false)) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f83])).
% 1.10/0.45 thf(f86,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : ((((cT @ X0)) != $true) | (((cT @ X1)) = $true) | (((cT @ (imp @ X0 @ X1))) = $false)) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f82])).
% 1.10/0.45 thf(f218,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ X2))) | ($false = ((cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X0)) @ X2))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f86,f8])).
% 1.10/0.45 thf(f219,plain,(
% 1.10/0.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ X3))) | ($false = ((cT @ (imp @ (imp @ X0 @ (imp @ X1 @ (imp @ X2 @ X1))) @ X3))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f86,f40])).
% 1.10/0.45 thf(f236,plain,(
% 1.10/0.45 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ (imp @ X0 @ (imp @ X1 @ (imp @ X2 @ X1))) @ X3)))) | ($true = ((cT @ X3)))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f219])).
% 1.10/0.45 thf(f237,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X0)) @ X2)))) | ($true = ((cT @ X2)))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f218])).
% 1.10/0.45 thf(f1237,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X0)))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f237,f9])).
% 1.10/0.45 thf(f1245,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((cT @ (imp @ X0 @ (imp @ X1 @ X2))))) | ($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f7,f9])).
% 1.10/0.45 thf(f1250,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((cT @ (imp @ X0 @ (imp @ X1 @ X2))))) | ($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f1245])).
% 1.10/0.45 thf(f1258,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X0)))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f1237])).
% 1.10/0.45 thf(f1277,plain,(
% 1.10/0.45 ( ! [X0 : $i] : (($true = $false) | ($true = ((cT @ (imp @ X0 @ X0))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f236,f1258])).
% 1.10/0.45 thf(f1294,plain,(
% 1.10/0.45 ( ! [X0 : $i] : (($true = ((cT @ (imp @ X0 @ X0))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f1277])).
% 1.10/0.45 thf(f1327,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cT @ X1)) = $true) | ($false = ((cT @ (imp @ (imp @ X0 @ X0) @ X1))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f86,f1294])).
% 1.10/0.45 thf(f1330,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ (imp @ X0 @ X0) @ X1)))) | (((cT @ X1)) = $true)) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f1327])).
% 1.10/0.45 thf(f1879,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2))))) | ($false = ((cT @ (imp @ X0 @ (imp @ X1 @ X2)))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f1250,f13])).
% 1.10/0.45 thf(f1883,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2))))) | ($false = ((cT @ (imp @ X1 @ X2))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f1250,f85])).
% 1.10/0.45 thf(f1923,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2))))) | ($false = ((cT @ (imp @ X1 @ X2))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f1883])).
% 1.10/0.45 thf(f1926,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2))))) | ($false = ((cT @ (imp @ X0 @ (imp @ X1 @ X2)))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f1879])).
% 1.10/0.45 thf(f4081,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($true = ((cT @ (imp @ X0 @ X2)))) | ($false = ((cT @ (imp @ (imp @ X1 @ X0) @ X2))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f237,f1923])).
% 1.10/0.45 thf(f4126,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ (imp @ X1 @ X0) @ X2)))) | ($true = ((cT @ (imp @ X0 @ X2))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f4081])).
% 1.10/0.45 thf(f4173,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((cT @ (imp @ (nt @ X1) @ (imp @ X1 @ X0)))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f10,f4126])).
% 1.10/0.45 thf(f4243,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ (nt @ X1) @ (imp @ X1 @ X0)))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f4173])).
% 1.10/0.45 thf(f4289,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cT @ X2))) | ($false = ((cT @ (imp @ (imp @ (nt @ X0) @ (imp @ X0 @ X1)) @ X2))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f86,f4243])).
% 1.10/0.45 thf(f4292,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ (imp @ (nt @ X0) @ (imp @ X0 @ X1)) @ X2)))) | ($true = ((cT @ X2)))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f4289])).
% 1.10/0.45 thf(f9045,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (((cT @ (imp @ X0 @ X1))) = $true) | ($false = ((cT @ (imp @ X0 @ (imp @ X0 @ X1)))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f1330,f1926])).
% 1.10/0.45 thf(f9102,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ X0 @ (imp @ X0 @ X1))))) | (((cT @ (imp @ X0 @ X1))) = $true)) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f9045])).
% 1.10/0.45 thf(f10055,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((cT @ (imp @ (imp @ X0 @ X1) @ X2)))) | ($true = ((cT @ (imp @ (nt @ X0) @ X2))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f1923,f4292])).
% 1.10/0.45 thf(f10145,plain,(
% 1.10/0.45 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((cT @ (imp @ (imp @ X0 @ X1) @ X2)))) | ($true = ((cT @ (imp @ (nt @ X0) @ X2))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f10055])).
% 1.10/0.45 thf(f10677,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((cT @ (imp @ (nt @ (nt @ X0)) @ (imp @ X1 @ X0)))))) )),
% 1.10/0.45 inference(constrained_superposition,[],[f10,f10145])).
% 1.10/0.45 thf(f10768,plain,(
% 1.10/0.45 ( ! [X0 : $i,X1 : $i] : (($true = ((cT @ (imp @ (nt @ (nt @ X0)) @ (imp @ X1 @ X0)))))) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f10677])).
% 1.10/0.45 thf(f10831,plain,(
% 1.10/0.45 ( ! [X0 : $i] : (($true = $false) | (((cT @ (imp @ (nt @ (nt @ X0)) @ X0))) = $true)) )),
% 1.10/0.45 inference(constrained_superposition,[],[f9102,f10768])).
% 1.10/0.45 thf(f10852,plain,(
% 1.10/0.45 ( ! [X0 : $i] : ((((cT @ (imp @ (nt @ (nt @ X0)) @ X0))) = $true)) )),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f10831])).
% 1.10/0.45 thf(f10880,plain,(
% 1.10/0.45 ($true != $true)),
% 1.10/0.45 inference(constrained_superposition,[],[f11,f10852])).
% 1.10/0.45 thf(f10925,plain,(
% 1.10/0.45 $false),
% 1.10/0.45 inference(trivial_inequality_removal,[],[f10880])).
% 1.10/0.45 % SZS output end Proof for theBenchmark
% 1.10/0.45 % (837458)------------------------------
% 1.10/0.45 % (837458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.45 % (837458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.45 % (837458)CaDiCaL version: 2.1.3
% 1.10/0.45 % (837458)Termination reason: Refutation
% 1.10/0.45 % (837458)Time elapsed: 0.220 s
% 1.10/0.45 % (837458)Peak memory usage: 15 MB
% 1.10/0.45 % (837458)Instructions burned: 849 (million)
% 1.10/0.45 % (837451)Success in time 0.249 s
% 1.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------