%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM762^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:19:29 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM762^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n011.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 12:53:16 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36 % (44269)Will run a generic schedule for satisfiability detection.
% 0.20/0.36 % (44275)% WARNING: option uhcvi not known.
% 0.20/0.36 % (44275)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1702519093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.36 % (44274)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1933539754_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.36 % (44278)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=676549211:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.36 % (44276)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2217949558:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.36 % (44277)dis+10_1_sil=32000:sp=arity:random_seed=1551314130:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.36 % (44278)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (44275)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (44275)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % (44279)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1777403542:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (44280)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=88844779:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.36 % (44286)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2853129709:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (44290)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3904075683:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (44277)Instruction limit reached!
% 0.20/0.36 % (44277)------------------------------
% 0.20/0.36 % (44277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (44277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (44277)CaDiCaL version: 2.1.3
% 0.20/0.36 % (44277)Termination reason: Instruction limit
% 0.20/0.36 % (44277)Termination phase: Saturation
% 0.20/0.36 % (44277)Time elapsed: 0.052 s
% 0.20/0.36 % (44277)Peak memory usage: 12 MB
% 0.20/0.36 % (44277)Instructions burned: 104 (million)
% 0.20/0.36 % (44278)Instruction limit reached!
% 0.20/0.36 % (44278)------------------------------
% 0.20/0.36 % (44278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (44278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (44278)CaDiCaL version: 2.1.3
% 0.20/0.36 % (44278)Termination reason: Instruction limit
% 0.20/0.36 % (44278)Termination phase: Saturation
% 0.20/0.36 % (44278)Time elapsed: 0.056 s
% 0.20/0.36 % (44278)Peak memory usage: 12 MB
% 0.20/0.36 % (44278)Instructions burned: 117 (million)
% 0.20/0.36 % (44292)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=4179805852:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.36 % (44279)Instruction limit reached!
% 0.20/0.36 % (44279)------------------------------
% 0.20/0.36 % (44279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (44279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (44279)CaDiCaL version: 2.1.3
% 0.20/0.36 % (44279)Termination reason: Instruction limit
% 0.20/0.36 % (44279)Termination phase: Saturation
% 0.20/0.36 % (44279)Time elapsed: 0.067 s
% 0.20/0.36 % (44279)Peak memory usage: 12 MB
% 0.20/0.36 % (44279)Instructions burned: 132 (million)
% 0.20/0.36 % (44292)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (44292)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % (44293)ott-21_1_sil=16000:fs=off:random_seed=3871109091:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.36 % (44280)Instruction limit reached!
% 0.20/0.36 % (44280)------------------------------
% 0.20/0.36 % (44280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (44280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (44280)CaDiCaL version: 2.1.3
% 0.20/0.36 % (44280)Termination reason: Instruction limit
% 0.20/0.36 % (44280)Termination phase: Saturation
% 0.20/0.36 % (44280)Time elapsed: 0.079 s
% 0.20/0.36 % (44280)Peak memory usage: 12 MB
% 0.20/0.36 % (44280)Instructions burned: 160 (million)
% 0.20/0.36 % (44290) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-44269-44290"...
% 0.20/0.36 % (44290)...printing done.
% 0.20/0.36 % (44290)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% 0.20/0.36 thf(type_def_5, type, frac: $tType).
% 0.20/0.36 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.36 thf(func_def_0, type, x: frac).
% 0.20/0.36 thf(func_def_1, type, y: frac).
% 0.20/0.36 thf(func_def_2, type, z: frac).
% 0.20/0.36 thf(func_def_3, type, u: frac).
% 0.20/0.36 thf(func_def_4, type, moref: (frac > frac > $o)).
% 0.20/0.36 thf(func_def_6, type, eq: (frac > frac > $o)).
% 0.20/0.36 thf(func_def_7, type, pf: (frac > frac > frac)).
% 0.20/0.36 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.20/0.36 thf(f1,axiom,(
% 0.20/0.36 (moref @ x @ y)),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m)).
% 0.20/0.36 thf(f2,axiom,(
% 0.20/0.36 ~(moref @ z @ u) => (eq @ z @ u)),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 0.20/0.36 thf(f4,axiom,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44)).
% 0.20/0.36 thf(f5,axiom,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz61)).
% 0.20/0.36 thf(f6,axiom,(
% 0.20/0.36 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37)).
% 0.20/0.36 thf(f7,axiom,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56)).
% 0.20/0.36 thf(f8,axiom,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz64)).
% 0.20/0.36 thf(f9,conjecture,(
% 0.20/0.36 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.20/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65b)).
% 0.20/0.36 thf(f10,negated_conjecture,(
% 0.20/0.36 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.20/0.36 inference(negated_conjecture,[status(cth)],[f9])).
% 0.20/0.36 thf(f11,plain,(
% 0.20/0.36 (moref @ x @ y)),
% 0.20/0.36 inference(rectify,[],[f1])).
% 0.20/0.36 thf(f12,plain,(
% 0.20/0.36 (((moref @ x @ y)) = $true)),
% 0.20/0.36 inference(fool_elimination,[],[f11])).
% 0.20/0.36 thf(f13,plain,(
% 0.20/0.36 ~(moref @ z @ u) => (eq @ z @ u)),
% 0.20/0.36 inference(rectify,[],[f2])).
% 0.20/0.36 thf(f14,plain,(
% 0.20/0.36 ~ (((moref @ z @ u)) = $true) => (((eq @ z @ u)) = $true)),
% 0.20/0.36 inference(fool_elimination,[],[f13])).
% 0.20/0.36 thf(f17,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((eq @ X0 @ X2) => ((eq @ X1 @ X3) => (moref @ X2 @ X3))))),
% 0.20/0.36 inference(rectify,[],[f4])).
% 0.20/0.36 thf(f18,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X0 @ X1)) = $true) => ((((eq @ X0 @ X2)) = $true) => ((((eq @ X1 @ X3)) = $true) => (((moref @ X2 @ X3)) = $true))))),
% 0.20/0.36 inference(fool_elimination,[],[f17])).
% 0.20/0.36 thf(f19,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac] : ((moref @ X0 @ X1) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2)))),
% 0.20/0.36 inference(rectify,[],[f5])).
% 0.20/0.36 thf(f20,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ X0 @ X1)) = $true) => (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true))),
% 0.20/0.36 inference(fool_elimination,[],[f19])).
% 0.20/0.36 thf(f21,plain,(
% 0.20/0.36 ! [X0 : frac] : (eq @ X0 @ X0)),
% 0.20/0.36 inference(rectify,[],[f6])).
% 0.20/0.36 thf(f22,plain,(
% 0.20/0.36 ! [X0 : frac] : (((eq @ X0 @ X0)) = $true)),
% 0.20/0.36 inference(fool_elimination,[],[f21])).
% 0.20/0.36 thf(f23,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.36 inference(rectify,[],[f7])).
% 0.20/0.36 thf(f24,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X0 @ X1)) = $true) => ((((eq @ X2 @ X3)) = $true) => (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 0.20/0.36 inference(fool_elimination,[],[f23])).
% 0.20/0.36 thf(f25,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.36 inference(rectify,[],[f8])).
% 0.20/0.36 thf(f26,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X0 @ X1)) = $true) => ((((moref @ X2 @ X3)) = $true) => (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 0.20/0.36 inference(fool_elimination,[],[f25])).
% 0.20/0.36 thf(f27,plain,(
% 0.20/0.36 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.20/0.36 inference(rectify,[],[f10])).
% 0.20/0.36 thf(f28,plain,(
% 0.20/0.36 ~ (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $true)),
% 0.20/0.36 inference(fool_elimination,[],[f27])).
% 0.20/0.36 thf(f29,plain,(
% 0.20/0.36 (((moref @ z @ u)) != $true) => (((eq @ z @ u)) = $true)),
% 0.20/0.36 inference(flattening,[],[f14])).
% 0.20/0.36 thf(f31,plain,(
% 0.20/0.36 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.20/0.36 inference(flattening,[],[f28])).
% 0.20/0.36 thf(f32,plain,(
% 0.20/0.36 (((eq @ z @ u)) = $true) | (((moref @ z @ u)) = $true)),
% 0.20/0.36 inference(ennf_transformation,[],[f29])).
% 0.20/0.36 thf(f34,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((((moref @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true)) | (((eq @ X0 @ X2)) != $true)) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(ennf_transformation,[],[f18])).
% 0.20/0.36 thf(f35,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X2 @ X3)) = $true) | (((eq @ X1 @ X3)) != $true) | (((eq @ X0 @ X2)) != $true) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(flattening,[],[f34])).
% 0.20/0.36 thf(f36,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(ennf_transformation,[],[f20])).
% 0.20/0.36 thf(f37,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true)) | (((eq @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(ennf_transformation,[],[f24])).
% 0.20/0.36 thf(f38,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((eq @ X2 @ X3)) != $true) | (((eq @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(flattening,[],[f37])).
% 0.20/0.36 thf(f39,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true)) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(ennf_transformation,[],[f26])).
% 0.20/0.36 thf(f40,plain,(
% 0.20/0.36 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.36 inference(flattening,[],[f39])).
% 0.20/0.36 thf(f41,plain,(
% 0.20/0.36 (((moref @ x @ y)) = $true)),
% 0.20/0.36 inference(cnf_transformation,[],[f12])).
% 0.20/0.36 thf(f42,plain,(
% 0.20/0.36 (((eq @ z @ u)) = $true) | (((moref @ z @ u)) = $true)),
% 0.20/0.36 inference(cnf_transformation,[],[f32])).
% 0.20/0.36 thf(f44,plain,(
% 0.20/0.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((eq @ X1 @ X3)) != $true) | (((eq @ X0 @ X2)) != $true) | (((moref @ X2 @ X3)) = $true)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f35])).
% 0.20/0.36 thf(f45,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X2))) = $true)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f36])).
% 0.20/0.36 thf(f46,plain,(
% 0.20/0.36 ( ! [X0 : frac] : ((((eq @ X0 @ X0)) = $true)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f22])).
% 0.20/0.36 thf(f47,plain,(
% 0.20/0.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((eq @ X0 @ X1)) != $true) | (((eq @ X2 @ X3)) != $true) | (((eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f38])).
% 0.20/0.36 thf(f48,plain,(
% 0.20/0.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | (((moref @ X2 @ X3)) != $true) | (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)) )),
% 0.20/0.36 inference(cnf_transformation,[],[f40])).
% 0.20/0.36 thf(f49,plain,(
% 0.20/0.36 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.20/0.36 inference(cnf_transformation,[],[f31])).
% 0.20/0.36 thf(f51,definition,(
% 0.20/0.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.36 thf(f54,definition,(
% 0.20/0.36 spl0_1 <=> (((moref @ z @ u)) = $true)),
% 0.20/0.36 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.20/0.36 thf(f56,plain,(
% 0.20/0.36 (((moref @ z @ u)) = $true) | ~spl0_1),
% 0.20/0.36 inference(avatar_component_clause,[],[f54])).
% 0.20/0.36 thf(f58,definition,(
% 0.20/0.36 spl0_2 <=> (((eq @ z @ u)) = $true)),
% 0.20/0.36 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.20/0.36 thf(f60,plain,(
% 0.20/0.36 (((eq @ z @ u)) = $true) | ~spl0_2),
% 0.20/0.36 inference(avatar_component_clause,[],[f58])).
% 0.20/0.36 thf(f61,plain,(
% 0.20/0.36 spl0_1 | spl0_2),
% 0.20/0.36 inference(avatar_split_clause,[],[f42,f58,f54])).
% 0.20/0.36 thf(f64,plain,(
% 0.20/0.36 ($true != $true) | (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $false)),
% 0.20/0.36 inference(constrained_superposition,[],[f49,f51])).
% 0.20/0.36 thf(f66,plain,(
% 0.20/0.36 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $false)),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f64])).
% 0.20/0.36 thf(f75,plain,(
% 0.20/0.36 ( ! [X0 : frac] : (($true != $true) | ($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.20/0.36 inference(constrained_superposition,[],[f45,f41])).
% 0.20/0.36 thf(f77,plain,(
% 0.20/0.36 ( ! [X0 : frac] : (($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X0))))) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.36 thf(f80,plain,(
% 0.20/0.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true != ((eq @ X1 @ X2))) | ($true != ((eq @ X0 @ X3))) | ($true = ((moref @ X3 @ X2))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(constrained_superposition,[],[f44,f51])).
% 0.20/0.36 thf(f86,plain,(
% 0.20/0.36 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X0 @ X3))) | ($true != ((eq @ X1 @ X2))) | ($true = ((moref @ X3 @ X2))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f80])).
% 0.20/0.36 thf(f94,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true != ((eq @ X1 @ X2))) | ($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X0 @ X2))))) )),
% 0.20/0.36 inference(constrained_superposition,[],[f47,f46])).
% 0.20/0.36 thf(f97,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X1 @ X2))) | ($true = ((eq @ (pf @ X0 @ X1) @ (pf @ X0 @ X2))))) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f94])).
% 0.20/0.36 thf(f106,plain,(
% 0.20/0.36 ( ! [X0 : frac,X1 : frac] : (($true != $true) | (((moref @ X0 @ X1)) != $true) | ($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X1))))) )),
% 0.20/0.36 inference(constrained_superposition,[],[f48,f41])).
% 0.20/0.36 thf(f110,plain,(
% 0.20/0.36 ( ! [X0 : frac,X1 : frac] : ((((moref @ X0 @ X1)) != $true) | ($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X1))))) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f106])).
% 0.20/0.36 thf(f143,plain,(
% 0.20/0.36 ( ! [X0 : frac] : (($true != $true) | ($true = ((eq @ (pf @ X0 @ z) @ (pf @ X0 @ u))))) ) | ~spl0_2),
% 0.20/0.36 inference(constrained_superposition,[],[f97,f60])).
% 0.20/0.36 thf(f144,plain,(
% 0.20/0.36 ( ! [X0 : frac] : (($true = ((eq @ (pf @ X0 @ z) @ (pf @ X0 @ u))))) ) | ~spl0_2),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f143])).
% 0.20/0.36 thf(f148,plain,(
% 0.20/0.36 ( ! [X0 : frac,X1 : frac] : (($true != $true) | ($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X1)))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(constrained_superposition,[],[f110,f51])).
% 0.20/0.36 thf(f158,plain,(
% 0.20/0.36 ( ! [X0 : frac,X1 : frac] : (($true = ((moref @ (pf @ x @ X0) @ (pf @ y @ X1)))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f148])).
% 0.20/0.36 thf(f161,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true != ((eq @ X1 @ X2))) | ($true = ((moref @ X0 @ X2))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(constrained_superposition,[],[f86,f46])).
% 0.20/0.36 thf(f170,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != ((eq @ X1 @ X2))) | ($true = ((moref @ X0 @ X2))) | (((moref @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f161])).
% 0.20/0.36 thf(f235,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true != $true) | ($true = ((moref @ X2 @ X1))) | ($false = ((moref @ X2 @ X0))) | (((eq @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(constrained_superposition,[],[f170,f51])).
% 0.20/0.36 thf(f248,plain,(
% 0.20/0.36 ( ! [X2 : frac,X0 : frac,X1 : frac] : (($true = ((moref @ X2 @ X1))) | ($false = ((moref @ X2 @ X0))) | (((eq @ X0 @ X1)) = $false)) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f235])).
% 0.20/0.36 thf(f255,plain,(
% 0.20/0.36 ($true = $false) | (((moref @ z @ u)) = $false)),
% 0.20/0.36 inference(constrained_superposition,[],[f66,f158])).
% 0.20/0.36 thf(f256,plain,(
% 0.20/0.36 (((moref @ z @ u)) = $false)),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f255])).
% 0.20/0.36 thf(f375,plain,(
% 0.20/0.36 ( ! [X0 : frac] : (($true = $false) | ($false = ((moref @ (pf @ x @ z) @ X0))) | ($false = ((eq @ X0 @ (pf @ y @ u))))) )),
% 0.20/0.36 inference(constrained_superposition,[],[f66,f248])).
% 0.20/0.36 thf(f413,plain,(
% 0.20/0.36 ( ! [X0 : frac] : (($false = ((moref @ (pf @ x @ z) @ X0))) | ($false = ((eq @ X0 @ (pf @ y @ u))))) )),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f375])).
% 0.20/0.36 thf(f460,plain,(
% 0.20/0.36 ($true = $false) | ($false = ((moref @ (pf @ x @ z) @ (pf @ y @ z)))) | ~spl0_2),
% 0.20/0.36 inference(constrained_superposition,[],[f413,f144])).
% 0.20/0.36 thf(f485,plain,(
% 0.20/0.36 ($false = ((moref @ (pf @ x @ z) @ (pf @ y @ z)))) | ~spl0_2),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f460])).
% 0.20/0.36 thf(f509,plain,(
% 0.20/0.36 ($true = $false) | ~spl0_2),
% 0.20/0.36 inference(forward_demodulation,[],[f485,f77])).
% 0.20/0.36 thf(f510,plain,(
% 0.20/0.36 $false | ~spl0_2),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f509])).
% 0.20/0.36 thf(f511,plain,(
% 0.20/0.36 ~spl0_2),
% 0.20/0.36 inference(avatar_contradiction_clause,[],[f510])).
% 0.20/0.36 thf(f514,plain,(
% 0.20/0.36 ($true = $false) | ~spl0_1),
% 0.20/0.36 inference(forward_demodulation,[],[f56,f256])).
% 0.20/0.36 thf(f515,plain,(
% 0.20/0.36 $false | ~spl0_1),
% 0.20/0.36 inference(trivial_inequality_removal,[],[f514])).
% 0.20/0.36 thf(f516,plain,(
% 0.20/0.36 ~spl0_1),
% 0.20/0.36 inference(avatar_contradiction_clause,[],[f515])).
% 0.20/0.36 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f61])).
% 0.20/0.36 cnf(s9, plain, ~spl0_2, inference(sat_conversion,[],[f511])).
% 0.20/0.36 cnf(s12, plain, ~spl0_1, inference(sat_conversion,[],[f516])).
% 0.20/0.36 cnf(s13, plain, $false, inference(rat,[],[s1,s9,s12])).
% 0.20/0.36 thf(f517,plain,(
% 0.20/0.36 $false),
% 0.20/0.36 inference(avatar_sat_refutation,[],[s13])).
% 0.20/0.36 % SZS output end Proof for theBenchmark
% 0.20/0.36 % (44290)------------------------------
% 0.20/0.36 % (44290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (44290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (44290)CaDiCaL version: 2.1.3
% 0.20/0.36 % (44290)Termination reason: Refutation
% 0.20/0.36 % (44290)Time elapsed: 0.050 s
% 0.20/0.36 % (44290)Peak memory usage: 13 MB
% 0.20/0.36 % (44290)Instructions burned: 93 (million)
% 0.20/0.36 % (44269)Success in time 0.124 s
% 0.20/0.36 % Vampire exiting
%------------------------------------------------------------------------------