%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 11:40:29 AM UTC 2026
% Result : Unsatisfiable 16.50s 3.38s
% Output : Refutation 16.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 49 ( 49 unt; 7 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-4 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq3(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
fof(f4,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f7,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
fof(f8,axiom,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
fof(f9,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f11,axiom,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f23,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
fof(f24,axiom,
! [X2,X0,X1] : ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
fof(f25,plain,
! [X2,X0,X1] : true = ifeq(leq(X0,addition(multiplication(X1,X0),X2)),true,leq(X0,multiplication(strong_iteration(X1),X2)),true),
inference(reorient_equations,[],[f24]) ).
fof(f28,axiom,
! [X0,X1] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f29,plain,
! [X0,X1] : true = ifeq3(addition(X0,X1),X1,leq(X0,X1),true),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f31,plain,
true != leq(multiplication(sK2_goals_X0,strong_iteration(multiplication(sK1_goals_X1,sK2_goals_X0))),multiplication(strong_iteration(multiplication(sK2_goals_X0,sK1_goals_X1)),sK2_goals_X0)),
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF0 = multiplication(sK1_goals_X1,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f33,plain,
multiplication(sK1_goals_X1,sK2_goals_X0) = sF0,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF1 = strong_iteration(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f35,plain,
strong_iteration(sF0) = sF1,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF2 = multiplication(sK2_goals_X0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f37,plain,
multiplication(sK2_goals_X0,sF1) = sF2,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF3 = multiplication(sK2_goals_X0,sK1_goals_X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f39,plain,
multiplication(sK2_goals_X0,sK1_goals_X1) = sF3,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF4 = strong_iteration(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f41,plain,
strong_iteration(sF3) = sF4,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF5 = multiplication(sF4,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f43,plain,
multiplication(sF4,sK2_goals_X0) = sF5,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF6 = leq(sF2,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f45,plain,
leq(sF2,sF5) = sF6,
inference(reorient_equations,[],[f44]) ).
fof(f46,plain,
true != sF6,
inference(definition_folding,[],[f31,f45,f43,f41,f39,f37,f35,f33]) ).
fof(f47,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[],[f23,f4]) ).
fof(f78,plain,
sF1 = addition(one,multiplication(sF0,sF1)),
inference(superposition,[],[f47,f35]) ).
fof(f83,plain,
! [X0] : multiplication(sF3,X0) = multiplication(sK2_goals_X0,multiplication(sK1_goals_X1,X0)),
inference(superposition,[],[f8,f39]) ).
fof(f85,plain,
! [X0] : multiplication(sF0,X0) = multiplication(sK1_goals_X1,multiplication(sK2_goals_X0,X0)),
inference(superposition,[],[f8,f33]) ).
fof(f155,plain,
! [X2,X0,X1] : true = ifeq(leq(X2,addition(X0,multiplication(X1,X2))),true,leq(X2,multiplication(strong_iteration(X1),X0)),true),
inference(superposition,[],[f25,f4]) ).
fof(f161,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f11,f9]) ).
fof(f364,plain,
multiplication(sF0,sF1) = multiplication(sK1_goals_X1,sF2),
inference(superposition,[],[f85,f37]) ).
fof(f1187,plain,
! [X0] : true = ifeq3(X0,X0,leq(X0,X0),true),
inference(superposition,[],[f29,f7]) ).
fof(f1202,plain,
! [X0] : true = leq(X0,X0),
inference(forward_demodulation,[],[f1187,f1]) ).
fof(f2657,plain,
! [X0] : multiplication(X0,sF1) = addition(X0,multiplication(X0,multiplication(sF0,sF1))),
inference(superposition,[],[f161,f78]) ).
fof(f2680,plain,
! [X0] : multiplication(X0,sF1) = addition(X0,multiplication(X0,multiplication(sK1_goals_X1,sF2))),
inference(forward_demodulation,[],[f2657,f364]) ).
fof(f3413,plain,
multiplication(sK2_goals_X0,sF1) = addition(sK2_goals_X0,multiplication(sF3,sF2)),
inference(superposition,[],[f2680,f83]) ).
fof(f3491,plain,
sF2 = addition(sK2_goals_X0,multiplication(sF3,sF2)),
inference(forward_demodulation,[],[f3413,f37]) ).
fof(f3567,plain,
true = ifeq(leq(sF2,sF2),true,leq(sF2,multiplication(strong_iteration(sF3),sK2_goals_X0)),true),
inference(superposition,[],[f155,f3491]) ).
fof(f3592,plain,
true = ifeq(leq(sF2,sF2),true,leq(sF2,multiplication(sF4,sK2_goals_X0)),true),
inference(forward_demodulation,[],[f3567,f41]) ).
fof(f3593,plain,
true = ifeq(leq(sF2,sF2),true,leq(sF2,sF5),true),
inference(forward_demodulation,[],[f3592,f43]) ).
fof(f3594,plain,
true = ifeq(leq(sF2,sF2),true,sF6,true),
inference(forward_demodulation,[],[f3593,f45]) ).
fof(f3595,plain,
true = ifeq(true,true,sF6,true),
inference(forward_demodulation,[],[f3594,f1202]) ).
fof(f3596,plain,
true = sF6,
inference(forward_demodulation,[],[f3595,f3]) ).
fof(f3597,plain,
$false,
inference(forward_subsumption_resolution,[],[f3596,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE151-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 13:08:20 UTC 2026
% 0.15/0.38 % CPUTime :
% 0.15/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.94/3.19 % (2543654)Detected a unit-equality problem, will run specialized UEQ schedule.
% 15.94/3.19 % (2543677)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3186506006:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 15.94/3.19 % (2543680)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3783931833:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 15.94/3.19 % (2543676)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3670019254:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 15.94/3.19 % (2543674)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=4154492342:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 15.94/3.19 % (2543679)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=28327213:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 15.94/3.19 % (2543675)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=13301290:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 15.94/3.19 % (2543677)Instruction limit reached!
% 15.94/3.19 % (2543677)------------------------------
% 15.94/3.19 % (2543677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.94/3.19 % (2543677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.94/3.19 % (2543677)CaDiCaL version: 2.1.3
% 15.94/3.19 % (2543677)Termination reason: Instruction limit
% 15.94/3.19 % (2543677)Termination phase: Saturation
% 15.94/3.19 % (2543677)Time elapsed: 0.048 s
% 15.94/3.19 % (2543677)Peak memory usage: 89 MB
% 15.94/3.19 % (2543677)Instructions burned: 139 (million)
% 15.94/3.19 % (2543678)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2186654240:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 15.94/3.19 % (2543687)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=521222913:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 15.94/3.19 % (2543678)Instruction limit reached!
% 15.94/3.19 % (2543678)------------------------------
% 15.94/3.19 % (2543678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.94/3.19 % (2543678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.94/3.19 % (2543678)CaDiCaL version: 2.1.3
% 15.94/3.19 % (2543678)Termination reason: Instruction limit
% 15.94/3.19 % (2543678)Termination phase: Saturation
% 15.94/3.19 % (2543678)Time elapsed: 0.106 s
% 15.94/3.19 % (2543678)Peak memory usage: 90 MB
% 15.94/3.19 % (2543678)Instructions burned: 181 (million)
% 15.94/3.19 % (2543679)Instruction limit reached!
% 15.94/3.19 % (2543679)------------------------------
% 15.94/3.19 % (2543679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.94/3.19 % (2543679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.94/3.19 % (2543679)CaDiCaL version: 2.1.3
% 15.94/3.19 % (2543679)Termination reason: Instruction limit
% 15.94/3.19 % (2543679)Termination phase: Saturation
% 15.94/3.19 % (2543679)Time elapsed: 0.162 s
% 15.94/3.19 % (2543679)Peak memory usage: 90 MB
% 15.94/3.19 % (2543679)Instructions burned: 258 (million)
% 15.94/3.19 % (2543691)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2705674213:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 15.94/3.19 % (2543692)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=334582245:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 15.94/3.19 % (2543692)Instruction limit reached!
% 15.94/3.19 % (2543692)------------------------------
% 15.94/3.19 % (2543692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.94/3.19 % (2543692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.94/3.19 % (2543692)CaDiCaL version: 2.1.3
% 15.94/3.19 % (2543692)Termination reason: Instruction limit
% 15.94/3.19 % (2543692)Termination phase: Saturation
% 15.94/3.19 % (2543692)Time elapsed: 0.121 s
% 16.50/3.38 % (2543692)Peak memory usage: 91 MB
% 16.50/3.38 % (2543692)Instructions burned: 216 (million)
% 16.50/3.38 % (2543789)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=2172905478:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 16.50/3.38 % (2543680)Instruction limit reached!
% 16.50/3.38 % (2543680)------------------------------
% 16.50/3.38 % (2543680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.50/3.38 % (2543680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.50/3.38 % (2543680)CaDiCaL version: 2.1.3
% 16.50/3.38 % (2543680)Termination reason: Instruction limit
% 16.50/3.38 % (2543680)Termination phase: Saturation
% 16.50/3.38 % (2543680)Time elapsed: 0.650 s
% 16.50/3.38 % (2543680)Peak memory usage: 102 MB
% 16.50/3.38 % (2543680)Instructions burned: 1187 (million)
% 16.50/3.38 % (2543789)Instruction limit reached!
% 16.50/3.38 % (2543789)------------------------------
% 16.50/3.38 % (2543789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.50/3.38 % (2543789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.50/3.38 % (2543789)CaDiCaL version: 2.1.3
% 16.50/3.38 % (2543789)Termination reason: Instruction limit
% 16.50/3.38 % (2543789)Termination phase: Saturation
% 16.50/3.38 % (2543789)Time elapsed: 0.205 s
% 16.50/3.38 % (2543789)Peak memory usage: 94 MB
% 16.50/3.38 % (2543789)Instructions burned: 318 (million)
% 16.50/3.38 % (2543846)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2721417408:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 16.50/3.38 % (2543850)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3550359307:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 16.50/3.38 % (2543687)Instruction limit reached!
% 16.50/3.38 % (2543687)------------------------------
% 16.50/3.38 % (2543687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.50/3.38 % (2543687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.50/3.38 % (2543687)CaDiCaL version: 2.1.3
% 16.50/3.38 % (2543687)Termination reason: Instruction limit
% 16.50/3.38 % (2543687)Termination phase: Saturation
% 16.50/3.38 % (2543687)Time elapsed: 1.079 s
% 16.50/3.38 % (2543687)Peak memory usage: 142 MB
% 16.50/3.38 % (2543687)Instructions burned: 2051 (million)
% 16.50/3.38 % (2543853)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3951933775:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2986 on theBenchmark for (2986ds/14534Mi)
% 16.50/3.38 % (2543846)First to succeed.
% 16.50/3.38 % (2543846)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2543654"
% 16.50/3.38 % (2543846)Refutation found. Thanks to Tanya!
% 16.50/3.38 % SZS status Unsatisfiable for theBenchmark
% 16.50/3.38 % SZS output start Proof for theBenchmark
% See solution above
% 16.50/3.38 % (2543846)------------------------------
% 16.50/3.38 % (2543846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.50/3.38 % (2543846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.50/3.38 % (2543846)CaDiCaL version: 2.1.3
% 16.50/3.38 % (2543846)Termination reason: Refutation
% 16.50/3.38 % (2543846)Time elapsed: 1.048 s
% 16.50/3.38 % (2543846)Peak memory usage: 137 MB
% 16.50/3.38 % (2543846)Instructions burned: 1671 (million)
% 16.50/3.38 % (2543846)------------------------------
% 16.50/3.38 % (2543846)------------------------------
% 16.50/3.38 % (2543654)Success in time 2.234 s
% 16.50/3.38 % Vampire exiting
%------------------------------------------------------------------------------