%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:35:48 AM UTC 2026
% Result : Unsatisfiable 1.95s 0.62s
% Output : Refutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 71 ( 71 unt; 8 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 159 ( 159 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,negated_conjecture,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f14,axiom,
! [X0] : product(multiplicative_identity,X0,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f15,plain,
! [X0] : true = product(multiplicative_identity,X0,X0),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] : product(X0,multiplicative_identity,X0) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f17,plain,
! [X0] : true = product(X0,multiplicative_identity,X0),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f19,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true),
inference(reorient_equations,[],[f18]) ).
fof(f32,axiom,
! [X2,X3,X0,X1,X6,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X4,X6,X1),true,ifeq(sum(X3,X6,X0),true,sum(X5,X6,X2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
fof(f33,plain,
! [X2,X3,X0,X1,X6,X4,X5] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X4,X5),true,ifeq(sum(X4,X6,X1),true,ifeq(sum(X3,X6,X0),true,sum(X5,X6,X2),true),true),true),true),
inference(reorient_equations,[],[f32]) ).
fof(f34,axiom,
! [X0] : sum(inverse(X0),X0,multiplicative_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f35,plain,
! [X0] : true = sum(inverse(X0),X0,multiplicative_identity),
inference(reorient_equations,[],[f34]) ).
fof(f42,negated_conjecture,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f44,negated_conjecture,
sum(x,x,x) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_equalities) ).
fof(f45,plain,
true != sum(x,x,x),
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = ifeq2(X0,X0,X1,X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f47,plain,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
! [X2,X0,X1] : sF0(X0,X1,X2) = X1,
inference(definition_folding,[],[f1,f47]) ).
fof(f49,definition,
! [X0,X1] : sF1(X0,X1) = sum(X0,X1,add(X0,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f50,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = sF1(X0,X1),
inference(reorient_equations,[],[f49]) ).
fof(f51,plain,
! [X0,X1] : true = sF1(X0,X1),
inference(definition_folding,[],[f3,f50]) ).
fof(f61,definition,
! [X0] : sF5(X0) = product(multiplicative_identity,X0,X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f62,plain,
! [X0] : product(multiplicative_identity,X0,X0) = sF5(X0),
inference(reorient_equations,[],[f61]) ).
fof(f63,plain,
! [X0] : true = sF5(X0),
inference(definition_folding,[],[f15,f62]) ).
fof(f64,definition,
! [X0] : sF6(X0) = product(X0,multiplicative_identity,X0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f65,plain,
! [X0] : product(X0,multiplicative_identity,X0) = sF6(X0),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X0] : true = sF6(X0),
inference(definition_folding,[],[f17,f65]) ).
fof(f67,definition,
! [X0] : sF7(X0) = sum(inverse(X0),X0,multiplicative_identity),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f68,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity) = sF7(X0),
inference(reorient_equations,[],[f67]) ).
fof(f69,plain,
! [X0] : true = sF7(X0),
inference(definition_folding,[],[f35,f68]) ).
fof(f79,definition,
! [X2,X3,X0,X1] : sF11(X0,X1,X3,X2) = ifeq2(sum(X0,X1,X3),true,X3,X2),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f80,plain,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X3),true,X3,X2) = sF11(X0,X1,X3,X2),
inference(reorient_equations,[],[f79]) ).
fof(f81,definition,
! [X2,X3,X0,X1] : sF12(X0,X1,X2,X3) = ifeq2(sum(X0,X1,X2),true,sF11(X0,X1,X3,X2),X2),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f82,plain,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,sF11(X0,X1,X3,X2),X2) = sF12(X0,X1,X2,X3),
inference(reorient_equations,[],[f81]) ).
fof(f83,plain,
! [X2,X3,X0,X1] : sF12(X0,X1,X2,X3) = X2,
inference(definition_folding,[],[f42,f82,f80]) ).
fof(f89,definition,
sF15 = sum(x,x,x),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f90,plain,
sum(x,x,x) = sF15,
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
true != sF15,
inference(definition_folding,[],[f45,f90]) ).
fof(f93,plain,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,sF11(X0,X1,X3,X2),X2) = X2,
inference(forward_demodulation,[],[f83,f82]) ).
fof(f97,plain,
! [X0] : true = sum(inverse(X0),X0,multiplicative_identity),
inference(forward_demodulation,[],[f69,f68]) ).
fof(f98,plain,
! [X0] : true = product(X0,multiplicative_identity,X0),
inference(forward_demodulation,[],[f66,f65]) ).
fof(f99,plain,
! [X0] : true = product(multiplicative_identity,X0,X0),
inference(forward_demodulation,[],[f63,f62]) ).
fof(f102,plain,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
inference(forward_demodulation,[],[f48,f47]) ).
fof(f104,plain,
! [X2,X3,X0,X1] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(forward_demodulation,[],[f93,f80]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(true,true,ifeq(sum(multiplicative_identity,X3,X1),true,sum(X0,X4,X2),true),true),true),true),
inference(superposition,[],[f19,f98]) ).
fof(f126,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,ifeq(sum(multiplicative_identity,X4,X1),true,ifeq(sum(X3,X4,X0),true,sum(X3,X4,X2),true),true),true),true),
inference(superposition,[],[f33,f98]) ).
fof(f127,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(sum(multiplicative_identity,X4,X1),true,ifeq(sum(X3,X4,X0),true,sum(X3,X4,X2),true),true),true),
inference(forward_demodulation,[],[f126,f2]) ).
fof(f140,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(multiplicative_identity,X3,X1),true,sum(X0,X4,X2),true),true),true),
inference(forward_demodulation,[],[f109,f2]) ).
fof(f518,plain,
! [X0,X1] : ifeq2(sum(inverse(X0),X0,X1),true,ifeq2(true,true,multiplicative_identity,X1),X1) = X1,
inference(superposition,[],[f104,f97]) ).
fof(f520,plain,
! [X0,X1] : ifeq2(sum(inverse(X0),X0,X1),true,multiplicative_identity,X1) = X1,
inference(forward_demodulation,[],[f518,f102]) ).
fof(f721,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(sum(multiplicative_identity,X1,X0),true,ifeq(sum(X2,X1,multiplicative_identity),true,sum(X2,X1,X0),true),true),true),
inference(superposition,[],[f127,f99]) ).
fof(f752,plain,
! [X2,X0,X1] : true = ifeq(sum(multiplicative_identity,X1,X0),true,ifeq(sum(X2,X1,multiplicative_identity),true,sum(X2,X1,X0),true),true),
inference(forward_demodulation,[],[f721,f2]) ).
fof(f2537,plain,
! [X0,X1] : true = ifeq(sum(multiplicative_identity,X0,X1),true,ifeq(true,true,sum(inverse(X0),X0,X1),true),true),
inference(superposition,[],[f752,f97]) ).
fof(f2565,plain,
! [X0,X1] : true = ifeq(sum(multiplicative_identity,X0,X1),true,sum(inverse(X0),X0,X1),true),
inference(forward_demodulation,[],[f2537,f2]) ).
fof(f2598,plain,
! [X0] : true = ifeq(sF1(multiplicative_identity,X0),true,sum(inverse(X0),X0,add(multiplicative_identity,X0)),true),
inference(superposition,[],[f2565,f50]) ).
fof(f2618,plain,
! [X0] : true = ifeq(true,true,sum(inverse(X0),X0,add(multiplicative_identity,X0)),true),
inference(forward_demodulation,[],[f2598,f51]) ).
fof(f2622,plain,
! [X0] : true = sum(inverse(X0),X0,add(multiplicative_identity,X0)),
inference(forward_demodulation,[],[f2618,f2]) ).
fof(f2630,plain,
! [X0] : add(multiplicative_identity,X0) = ifeq2(true,true,multiplicative_identity,add(multiplicative_identity,X0)),
inference(superposition,[],[f520,f2622]) ).
fof(f2735,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[],[f2630,f102]) ).
fof(f2778,plain,
! [X0] : sF1(multiplicative_identity,X0) = sum(multiplicative_identity,X0,multiplicative_identity),
inference(superposition,[],[f50,f2735]) ).
fof(f2779,plain,
! [X0] : true = sum(multiplicative_identity,X0,multiplicative_identity),
inference(forward_demodulation,[],[f2778,f51]) ).
fof(f3742,plain,
! [X2,X0,X1] : true = ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(sum(multiplicative_identity,X1,multiplicative_identity),true,sum(X0,X2,X0),true),true),true),
inference(superposition,[],[f140,f98]) ).
fof(f3824,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(sum(multiplicative_identity,X1,multiplicative_identity),true,sum(X0,X2,X0),true),true),
inference(forward_demodulation,[],[f3742,f2]) ).
fof(f3833,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,sum(X0,X2,X0),true),true),
inference(forward_demodulation,[],[f3824,f2779]) ).
fof(f3837,plain,
! [X2,X0,X1] : true = ifeq(product(X0,X1,X2),true,sum(X0,X2,X0),true),
inference(forward_demodulation,[],[f3833,f2]) ).
fof(f3842,plain,
! [X0] : true = ifeq(true,true,sum(X0,X0,X0),true),
inference(superposition,[],[f3837,f98]) ).
fof(f3857,plain,
! [X0] : true = sum(X0,X0,X0),
inference(forward_demodulation,[],[f3842,f2]) ).
fof(f3862,plain,
true = sF15,
inference(superposition,[],[f3857,f90]) ).
fof(f4036,plain,
true != true,
inference(superposition,[],[f91,f3862]) ).
fof(f4044,plain,
$false,
inference(trivial_inequality_removal,[],[f4036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 21:02:49 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 1.95/0.62 % (3761892)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.95/0.62 % (3761900)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2965673185:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.95/0.62 % (3761902)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=271487954:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.95/0.62 % (3761897)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=3263471586:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.95/0.62 % (3761899)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1207866789:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.95/0.62 % (3761898)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=359984114:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.95/0.62 % (3761901)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=302525725:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.95/0.62 % (3761903)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=515129033:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.95/0.62 % (3761900)Instruction limit reached!
% 1.95/0.62 % (3761900)------------------------------
% 1.95/0.62 % (3761900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.95/0.62 % (3761900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.62 % (3761900)CaDiCaL version: 2.1.3
% 1.95/0.62 % (3761900)Termination reason: Instruction limit
% 1.95/0.62 % (3761900)Termination phase: Saturation
% 1.95/0.62 % (3761900)Time elapsed: 0.042 s
% 1.95/0.62 % (3761900)Peak memory usage: 89 MB
% 1.95/0.62 % (3761900)Instructions burned: 139 (million)
% 1.95/0.62 % (3761901)First to succeed.
% 1.95/0.62 % (3761901)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3761892"
% 1.95/0.62 % (3761902)Instruction limit reached!
% 1.95/0.62 % (3761902)------------------------------
% 1.95/0.62 % (3761902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.95/0.62 % (3761902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.62 % (3761902)CaDiCaL version: 2.1.3
% 1.95/0.62 % (3761902)Termination reason: Instruction limit
% 1.95/0.62 % (3761902)Termination phase: Saturation
% 1.95/0.62 % (3761902)Time elapsed: 0.084 s
% 1.95/0.62 % (3761902)Peak memory usage: 91 MB
% 1.95/0.62 % (3761902)Instructions burned: 258 (million)
% 1.95/0.62 % (3761911)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=624131090:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 1.95/0.62 % (3761912)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1951768188:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 1.95/0.62 % (3761901)Refutation found. Thanks to Tanya!
% 1.95/0.62 % SZS status Unsatisfiable for theBenchmark
% 1.95/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 2.44/0.72 % (3761901)------------------------------
% 2.44/0.72 % (3761901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.44/0.72 % (3761901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.72 % (3761901)CaDiCaL version: 2.1.3
% 2.44/0.72 % (3761901)Termination reason: Refutation
% 2.44/0.72 % (3761901)Time elapsed: 0.053 s
% 2.44/0.72 % (3761901)Peak memory usage: 90 MB
% 2.44/0.72 % (3761901)Instructions burned: 169 (million)
% 2.44/0.72 % (3761901)------------------------------
% 2.44/0.72 % (3761901)------------------------------
% 2.44/0.72 % (3761892)Success in time 0.313 s
% 2.44/0.72 % Vampire exiting
%------------------------------------------------------------------------------