%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:36:16 PM UTC 2026
% Result : Unsatisfiable 13.52s 2.89s
% Output : Refutation 13.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq4(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq3(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
fof(f5,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f15,axiom,
! [X2,X0,X1] : ifeq4(negate(add(X0,negate(add(X1,X2)))),negate(add(X1,negate(add(X0,X2)))),X0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] : ifeq2(positive_integer(X0),true,ifeq4(negate(add(X1,negate(X2))),X3,negate(add(X1,negate(add(X2,multiply(X0,add(X1,X3)))))),X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_4) ).
fof(f17,axiom,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
fof(f18,plain,
d = negate(add(negate(e),negate(add(d,negate(e))))),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
positive_integer(k) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_positive) ).
fof(f20,plain,
true = positive_integer(k),
inference(reorient_equations,[],[f19]) ).
fof(f21,axiom,
ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',base_step) ).
fof(f22,plain,
b = ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b),
inference(reorient_equations,[],[f21]) ).
fof(f25,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f39,plain,
! [X2,X3,X0,X1] : ifeq2(positive_integer(X2),true,ifeq4(negate(add(negate(X0),X1)),X3,negate(add(X1,negate(add(X0,multiply(X2,add(X1,X3)))))),X3),X3) = X3,
inference(superposition,[],[f16,f5]) ).
fof(f44,plain,
! [X2,X3,X0,X1] : ifeq2(positive_integer(X0),true,ifeq4(negate(add(X1,negate(X3))),X2,negate(add(X1,negate(add(multiply(X0,add(X1,X2)),X3)))),X2),X2) = X2,
inference(superposition,[],[f16,f5]) ).
fof(f54,plain,
! [X2,X0,X1] : ifeq4(negate(add(X1,negate(add(X2,X0)))),negate(add(X2,negate(add(X0,X1)))),X1,X2) = X2,
inference(superposition,[],[f15,f5]) ).
fof(f216,plain,
! [X2,X0,X1] : ifeq2(true,true,ifeq4(negate(add(X0,negate(X1))),X2,negate(add(X0,negate(add(multiply(k,add(X0,X2)),X1)))),X2),X2) = X2,
inference(superposition,[],[f44,f20]) ).
fof(f247,plain,
! [X2,X0,X1] : ifeq4(negate(add(X0,negate(X1))),X2,negate(add(X0,negate(add(multiply(k,add(X0,X2)),X1)))),X2) = X2,
inference(forward_demodulation,[],[f216,f3]) ).
fof(f315,plain,
! [X2,X0,X1] : ifeq4(negate(add(X1,negate(add(X2,X0)))),negate(add(negate(add(X0,X1)),X2)),X1,X2) = X2,
inference(superposition,[],[f54,f5]) ).
fof(f338,plain,
! [X0,X1] : ifeq2(positive_integer(X0),true,ifeq4(d,X1,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(X0,add(negate(add(d,negate(e))),X1)))))),X1),X1) = X1,
inference(superposition,[],[f39,f18]) ).
fof(f575,plain,
! [X0] : ifeq2(true,true,ifeq4(d,X0,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X0)))))),X0),X0) = X0,
inference(superposition,[],[f338,f20]) ).
fof(f584,plain,
! [X0] : ifeq4(d,X0,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X0)))))),X0) = X0,
inference(forward_demodulation,[],[f575,f3]) ).
fof(f1296,plain,
! [X0,X1] : negate(add(X0,negate(X1))) = negate(add(X0,negate(add(multiply(k,add(X0,negate(add(X0,negate(X1))))),X1)))),
inference(superposition,[],[f1,f247]) ).
fof(f1297,plain,
! [X0,X1] : negate(add(X0,negate(X1))) = negate(add(X0,negate(add(X1,multiply(k,add(X0,negate(add(X0,negate(X1))))))))),
inference(forward_demodulation,[],[f1296,f5]) ).
fof(f3629,plain,
d = negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),d)))))),
inference(superposition,[],[f1,f584]) ).
fof(f3630,plain,
d = negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),
inference(forward_demodulation,[],[f3629,f5]) ).
fof(f3640,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = ifeq4(negate(add(negate(e),negate(add(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),d)))),d,negate(e),negate(add(e,multiply(k,add(d,negate(add(d,negate(e)))))))),
inference(superposition,[],[f315,f3630]) ).
fof(f3784,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = ifeq4(negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),d,negate(e),negate(add(e,multiply(k,add(d,negate(add(d,negate(e)))))))),
inference(forward_demodulation,[],[f3640,f5]) ).
fof(f3812,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = ifeq4(negate(add(negate(e),negate(add(d,negate(e))))),d,negate(e),negate(add(e,multiply(k,add(d,negate(add(d,negate(e)))))))),
inference(forward_demodulation,[],[f3784,f1297]) ).
fof(f3825,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = ifeq4(d,d,negate(e),negate(add(e,multiply(k,add(d,negate(add(d,negate(e)))))))),
inference(forward_demodulation,[],[f3812,f18]) ).
fof(f3832,plain,
negate(e) = negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),
inference(forward_demodulation,[],[f3825,f1]) ).
fof(f3835,plain,
b = ifeq3(negate(e),negate(e),a,b),
inference(superposition,[],[f22,f3832]) ).
fof(f3926,plain,
a = b,
inference(forward_demodulation,[],[f3835,f2]) ).
fof(f3936,plain,
$false,
inference(forward_subsumption_resolution,[],[f3926,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n016.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 23:31:33 UTC 2026
% 0.04/0.40 % CPUTime :
% 0.04/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.44 Running first-order theorem proving
% 0.04/0.44 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
% 12.64/2.70 % (3111560)Detected a unit-equality problem, will run specialized UEQ schedule.
% 12.64/2.70 % (3111605)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=741809066:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 12.64/2.70 % (3111606)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1882294768:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 12.64/2.70 % (3111604)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=2823250329:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 12.64/2.70 % (3111610)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2265009225:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 12.64/2.70 % (3111608)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=67761273:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 12.64/2.70 % (3111607)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=587694286:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 12.64/2.70 % (3111609)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1948855674:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 12.64/2.70 % (3111607)Instruction limit reached!
% 12.64/2.70 % (3111607)------------------------------
% 12.64/2.70 % (3111607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.64/2.70 % (3111607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.64/2.70 % (3111607)CaDiCaL version: 2.1.3
% 12.64/2.70 % (3111607)Termination reason: Instruction limit
% 12.64/2.70 % (3111607)Termination phase: Saturation
% 12.64/2.70 % (3111607)Time elapsed: 0.083 s
% 12.64/2.70 % (3111607)Peak memory usage: 89 MB
% 12.64/2.70 % (3111607)Instructions burned: 137 (million)
% 12.64/2.70 % (3111608)Instruction limit reached!
% 12.64/2.70 % (3111608)------------------------------
% 12.64/2.70 % (3111608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.64/2.70 % (3111608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.64/2.70 % (3111608)CaDiCaL version: 2.1.3
% 12.64/2.70 % (3111608)Termination reason: Instruction limit
% 12.64/2.70 % (3111608)Termination phase: Saturation
% 12.64/2.70 % (3111608)Time elapsed: 0.095 s
% 12.64/2.70 % (3111608)Peak memory usage: 90 MB
% 12.64/2.70 % (3111608)Instructions burned: 181 (million)
% 12.64/2.70 % (3111609)Instruction limit reached!
% 12.64/2.70 % (3111609)------------------------------
% 12.64/2.70 % (3111609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.64/2.70 % (3111609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.64/2.70 % (3111609)CaDiCaL version: 2.1.3
% 12.64/2.70 % (3111609)Termination reason: Instruction limit
% 12.64/2.70 % (3111609)Termination phase: Saturation
% 12.64/2.70 % (3111609)Time elapsed: 0.152 s
% 12.64/2.70 % (3111609)Peak memory usage: 91 MB
% 12.64/2.70 % (3111609)Instructions burned: 257 (million)
% 12.64/2.70 % (3111618)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1122925530:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 12.64/2.70 % (3111619)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1300985502:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 12.64/2.70 % (3111620)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3644107777:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 12.64/2.70 % (3111620)Instruction limit reached!
% 12.64/2.70 % (3111620)------------------------------
% 12.64/2.70 % (3111620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.64/2.70 % (3111620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.64/2.70 % (3111620)CaDiCaL version: 2.1.3
% 12.64/2.70 % (3111620)Termination reason: Instruction limit
% 12.64/2.70 % (3111620)Termination phase: Saturation
% 12.64/2.70 % (3111620)Time elapsed: 0.108 s
% 13.52/2.89 % (3111620)Peak memory usage: 92 MB
% 13.52/2.89 % (3111620)Instructions burned: 216 (million)
% 13.52/2.89 % (3111624)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=3227938169: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)
% 13.52/2.89 % (3111610)Instruction limit reached!
% 13.52/2.89 % (3111610)------------------------------
% 13.52/2.89 % (3111610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.52/2.89 % (3111610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.52/2.89 % (3111610)CaDiCaL version: 2.1.3
% 13.52/2.89 % (3111610)Termination reason: Instruction limit
% 13.52/2.89 % (3111610)Termination phase: Saturation
% 13.52/2.89 % (3111610)Time elapsed: 0.566 s
% 13.52/2.89 % (3111610)Peak memory usage: 95 MB
% 13.52/2.89 % (3111610)Instructions burned: 1189 (million)
% 13.52/2.89 % (3111624)Instruction limit reached!
% 13.52/2.89 % (3111624)------------------------------
% 13.52/2.89 % (3111624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.52/2.89 % (3111624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.52/2.89 % (3111624)CaDiCaL version: 2.1.3
% 13.52/2.89 % (3111624)Termination reason: Instruction limit
% 13.52/2.89 % (3111624)Termination phase: Saturation
% 13.52/2.89 % (3111624)Time elapsed: 0.177 s
% 13.52/2.89 % (3111624)Peak memory usage: 91 MB
% 13.52/2.89 % (3111624)Instructions burned: 319 (million)
% 13.52/2.89 % (3111626)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=3510234068:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 13.52/2.89 % (3111628)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3131869343:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 13.52/2.89 % (3111619)First to succeed.
% 13.52/2.89 % (3111619)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3111560"
% 13.52/2.89 % (3111618)Instruction limit reached!
% 13.52/2.89 % (3111618)------------------------------
% 13.52/2.89 % (3111618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.52/2.89 % (3111618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.52/2.89 % (3111618)CaDiCaL version: 2.1.3
% 13.52/2.89 % (3111618)Termination reason: Instruction limit
% 13.52/2.89 % (3111618)Termination phase: Saturation
% 13.52/2.89 % (3111618)Time elapsed: 1.275 s
% 13.52/2.89 % (3111618)Peak memory usage: 142 MB
% 13.52/2.89 % (3111618)Instructions burned: 2053 (million)
% 13.52/2.89 % (3111631)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1281087528:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2983 on theBenchmark for (2983ds/14534Mi)
% 13.52/2.89 % (3111619)Refutation found. Thanks to Tanya!
% 13.52/2.89 % SZS status Unsatisfiable for theBenchmark
% 13.52/2.89 % SZS output start Proof for theBenchmark
% See solution above
% 13.52/2.89 % (3111619)------------------------------
% 13.52/2.89 % (3111619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.52/2.89 % (3111619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.52/2.89 % (3111619)CaDiCaL version: 2.1.3
% 13.52/2.89 % (3111619)Termination reason: Refutation
% 13.52/2.89 % (3111619)Time elapsed: 1.206 s
% 13.52/2.89 % (3111619)Peak memory usage: 140 MB
% 13.52/2.89 % (3111619)Instructions burned: 2008 (million)
% 13.52/2.89 % (3111619)------------------------------
% 13.52/2.89 % (3111619)------------------------------
% 13.52/2.89 % (3111560)Success in time 1.831 s
% 13.52/2.89 % Vampire exiting
%------------------------------------------------------------------------------