%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 09:07:31 AM UTC 2026
% Result : Unsatisfiable 0.18s 1.31s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X0,difference(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
fof(f3,axiom,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
fof(f4,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3_simplified) ).
fof(f5,plain,
! [X0,X1] : difference(X1,X0) = difference(difference(X1,X0),X0),
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X0,X1] : difference(X1,difference(X1,difference(X0,X1))) = difference(difference(X0,X1),difference(X0,X1)),
inference(superposition,[],[f2,f5]) ).
fof(f15,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X1)) = difference(X1,X1),
inference(forward_demodulation,[],[f10,f1]) ).
fof(f19,plain,
! [X0,X1] : difference(difference(X1,X0),difference(X1,X0)) = difference(difference(X0,difference(X0,X1)),difference(X0,difference(X0,X1))),
inference(superposition,[],[f15,f2]) ).
fof(f22,plain,
! [X0,X1] : difference(X0,X0) = difference(difference(X0,X0),difference(X1,X0)),
inference(superposition,[],[f5,f15]) ).
fof(f24,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X1)) = difference(difference(X1,X0),difference(X1,X0)),
inference(forward_demodulation,[],[f19,f15]) ).
fof(f26,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X1)) = difference(X0,X0),
inference(forward_demodulation,[],[f24,f15]) ).
fof(f84,plain,
! [X0,X1] : difference(X0,X0) = difference(X1,X1),
inference(superposition,[],[f26,f15]) ).
fof(f102,plain,
! [X2,X3,X0,X1] : difference(difference(difference(X0,X2),X3),difference(X1,X2)) = difference(difference(difference(X0,X1),X2),difference(X3,difference(X1,X2))),
inference(superposition,[],[f3,f3]) ).
fof(f105,plain,
! [X2,X0,X1] : difference(difference(X2,X1),difference(X1,X0)) = difference(difference(X2,difference(X1,X0)),difference(X0,difference(X0,X1))),
inference(superposition,[],[f3,f2]) ).
fof(f116,plain,
! [X0,X1] : difference(X0,X0) = difference(difference(X0,X1),X0),
inference(superposition,[],[f3,f22]) ).
fof(f124,plain,
! [X0,X1] : difference(X1,difference(X1,difference(X0,X1))) = difference(difference(X0,difference(X0,X1)),X1),
inference(superposition,[],[f2,f3]) ).
fof(f143,plain,
! [X0,X1] : difference(X1,X1) = difference(difference(X0,difference(X0,X1)),X1),
inference(forward_demodulation,[],[f124,f1]) ).
fof(f175,plain,
! [X0,X1] : difference(X1,difference(X0,X0)) = X1,
inference(superposition,[],[f1,f84]) ).
fof(f426,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X0)) = difference(X0,difference(X0,difference(X0,X1))),
inference(superposition,[],[f2,f116]) ).
fof(f428,plain,
! [X2,X0,X1] : difference(difference(X1,X0),difference(X0,X0)) = difference(difference(X1,difference(X0,X2)),X0),
inference(superposition,[],[f3,f116]) ).
fof(f438,plain,
! [X2,X0,X1] : difference(X1,X0) = difference(difference(X1,difference(X0,X2)),X0),
inference(forward_demodulation,[],[f428,f175]) ).
fof(f440,plain,
! [X0,X1] : difference(X0,X1) = difference(X0,difference(X0,difference(X0,X1))),
inference(forward_demodulation,[],[f426,f175]) ).
fof(f1256,plain,
! [X2,X0,X1] : difference(difference(X0,difference(X1,X2)),difference(X0,difference(X1,X2))) = difference(difference(X0,X1),difference(X0,difference(X1,X2))),
inference(superposition,[],[f116,f438]) ).
fof(f1265,plain,
! [X2,X0,X1] : difference(difference(X1,X2),difference(X1,X2)) = difference(difference(X0,X1),difference(X0,difference(X1,X2))),
inference(forward_demodulation,[],[f1256,f15]) ).
fof(f1286,plain,
! [X2,X0,X1] : difference(X1,X1) = difference(difference(X0,X1),difference(X0,difference(X1,X2))),
inference(forward_demodulation,[],[f1265,f26]) ).
fof(f1320,plain,
! [X0,X1] : difference(X1,X0) = difference(X1,difference(X0,difference(X0,X1))),
inference(superposition,[],[f440,f2]) ).
fof(f4590,plain,
! [X2,X0,X1] : difference(difference(X1,difference(X2,difference(X2,X0))),difference(X0,X0)) = difference(difference(X1,difference(X0,X0)),difference(X0,difference(X0,difference(X2,difference(X2,X0))))),
inference(superposition,[],[f105,f143]) ).
fof(f4936,plain,
! [X2,X0,X1] : difference(difference(X1,difference(X2,difference(X2,X0))),difference(X0,X0)) = difference(difference(X1,difference(X0,X0)),difference(X0,difference(X0,X2))),
inference(forward_demodulation,[],[f4590,f1320]) ).
fof(f5056,plain,
! [X2,X0,X1] : difference(X1,difference(X0,difference(X0,X2))) = difference(difference(X1,difference(X2,difference(X2,X0))),difference(X0,X0)),
inference(forward_demodulation,[],[f4936,f175]) ).
fof(f5131,plain,
! [X2,X0,X1] : difference(X1,difference(X2,difference(X2,X0))) = difference(X1,difference(X0,difference(X0,X2))),
inference(forward_demodulation,[],[f5056,f175]) ).
fof(f9652,plain,
! [X2,X0,X1] : difference(difference(X1,X0),difference(X1,X0)) = difference(X0,difference(X0,difference(difference(X1,X0),X2))),
inference(superposition,[],[f1286,f1]) ).
fof(f10050,plain,
! [X2,X0,X1] : difference(X0,X0) = difference(X0,difference(X0,difference(difference(X1,X0),X2))),
inference(forward_demodulation,[],[f9652,f15]) ).
fof(f16289,plain,
! [X2,X0,X1] : difference(X0,difference(X0,X0)) = difference(X0,difference(difference(X1,X0),X2)),
inference(superposition,[],[f440,f10050]) ).
fof(f16375,plain,
! [X2,X0,X1] : difference(X0,difference(difference(X1,X0),X2)) = X0,
inference(forward_demodulation,[],[f16289,f1]) ).
fof(f16551,plain,
! [X2,X0,X1] : difference(X1,X0) = difference(difference(X1,X0),difference(X0,X2)),
inference(superposition,[],[f16375,f1]) ).
fof(f20109,plain,
! [X2,X0,X1] : difference(difference(difference(X0,X2),X1),difference(X1,X2)) = difference(difference(difference(X0,X1),X2),difference(X2,difference(X2,X1))),
inference(superposition,[],[f102,f5131]) ).
fof(f20355,plain,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(difference(difference(X0,X2),X1),difference(X1,X2)),
inference(forward_demodulation,[],[f20109,f16551]) ).
fof(f20615,plain,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
inference(forward_demodulation,[],[f20355,f16551]) ).
fof(f21277,plain,
difference(difference(a,c),b) != difference(difference(a,c),b),
inference(superposition,[],[f4,f20615]) ).
fof(f21367,plain,
$false,
inference(trivial_inequality_removal,[],[f21277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n011.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 19:17:00 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running first-order theorem proving
% 0.10/0.19 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.12 % (3680895)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.75/1.12 % (3680905)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4232888490:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.75/1.12 % (3680902)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3331659554:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.75/1.12 % (3680903)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2534763738:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.75/1.12 % (3680901)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3738785322:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.75/1.12 % (3680904)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=103489055:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.75/1.12 % (3680900)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2162946856:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.75/1.12 % (3680906)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3745760385:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.75/1.12 % (3680905)Instruction limit reached!
% 4.75/1.12 % (3680905)------------------------------
% 4.75/1.12 % (3680905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.75/1.12 % (3680905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.75/1.12 % (3680905)CaDiCaL version: 2.1.3
% 4.75/1.12 % (3680905)Termination reason: Instruction limit
% 4.75/1.12 % (3680905)Termination phase: Saturation
% 4.75/1.12 % (3680905)Time elapsed: 0.081 s
% 4.75/1.12 % (3680905)Peak memory usage: 89 MB
% 4.75/1.12 % (3680905)Instructions burned: 260 (million)
% 4.75/1.12 % (3680903)Instruction limit reached!
% 4.75/1.12 % (3680903)------------------------------
% 4.75/1.12 % (3680903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.75/1.12 % (3680903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.75/1.12 % (3680903)CaDiCaL version: 2.1.3
% 4.75/1.12 % (3680903)Termination reason: Instruction limit
% 4.75/1.12 % (3680903)Termination phase: Saturation
% 4.75/1.12 % (3680903)Time elapsed: 0.079 s
% 4.75/1.12 % (3680903)Peak memory usage: 88 MB
% 4.75/1.12 % (3680903)Instructions burned: 137 (million)
% 4.75/1.12 % (3680904)Instruction limit reached!
% 4.75/1.12 % (3680904)------------------------------
% 4.75/1.12 % (3680904)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.75/1.12 % (3680904)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.75/1.12 % (3680904)CaDiCaL version: 2.1.3
% 4.75/1.12 % (3680904)Termination reason: Instruction limit
% 4.75/1.12 % (3680904)Termination phase: Saturation
% 4.75/1.12 % (3680904)Time elapsed: 0.098 s
% 4.75/1.12 % (3680904)Peak memory usage: 89 MB
% 4.75/1.12 % (3680904)Instructions burned: 182 (million)
% 4.75/1.12 % (3680914)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2852395858:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 4.75/1.12 % (3680915)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3163591672:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.75/1.12 % (3680916)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1309631229:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 4.75/1.12 % (3680916)Instruction limit reached!
% 4.75/1.12 % (3680916)------------------------------
% 4.75/1.12 % (3680916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.75/1.12 % (3680916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.75/1.12 % (3680916)CaDiCaL version: 2.1.3
% 4.75/1.12 % (3680916)Termination reason: Instruction limit
% 4.75/1.12 % (3680916)Termination phase: Saturation
% 4.75/1.12 % (3680916)Time elapsed: 0.107 s
% 0.18/1.31 % (3680916)Peak memory usage: 89 MB
% 0.18/1.31 % (3680916)Instructions burned: 217 (million)
% 0.18/1.31 % (3680906)First to succeed.
% 0.18/1.31 % (3680906)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3680895"
% 0.18/1.31 % (3680920)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3038174755:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 0.18/1.31 % (3680906)Refutation found. Thanks to Tanya!
% 0.18/1.31 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.31 % (3680906)------------------------------
% 0.18/1.31 % (3680906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.31 % (3680906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.31 % (3680906)CaDiCaL version: 2.1.3
% 0.18/1.31 % (3680906)Termination reason: Refutation
% 0.18/1.31 % (3680906)Time elapsed: 0.338 s
% 0.18/1.31 % (3680906)Peak memory usage: 93 MB
% 0.18/1.31 % (3680906)Instructions burned: 641 (million)
% 0.18/1.31 % (3680906)------------------------------
% 0.18/1.31 % (3680906)------------------------------
% 0.18/1.31 % (3680895)Success in time 0.728 s
% 0.18/1.31 % Vampire exiting
%------------------------------------------------------------------------------