%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN116-10 : 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 : n014.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 01:49:42 PM UTC 2026
% Result : Unsatisfiable 4.18s 1.37s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 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 : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f39,axiom,
l0(a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
fof(f40,plain,
true = l0(a),
inference(reorient_equations,[],[f39]) ).
fof(f61,axiom,
m0(b,b,e) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
fof(f62,plain,
true = m0(b,b,e),
inference(reorient_equations,[],[f61]) ).
fof(f73,axiom,
n0(b,a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
fof(f74,plain,
true = n0(b,a),
inference(reorient_equations,[],[f73]) ).
fof(f79,axiom,
! [X0,X1] : ifeq(n0(X0,X1),true,l1(X1,X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
fof(f80,plain,
! [X0,X1] : true = ifeq(n0(X0,X1),true,l1(X1,X1),true),
inference(reorient_equations,[],[f79]) ).
fof(f85,axiom,
! [X0,X1] : ifeq(m0(X0,X0,X1),true,m1(X1,X0,X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_005) ).
fof(f86,plain,
! [X0,X1] : true = ifeq(m0(X0,X0,X1),true,m1(X1,X0,X1),true),
inference(reorient_equations,[],[f85]) ).
fof(f247,axiom,
ifeq(l0(a),true,p1(a,a,a),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_088) ).
fof(f248,plain,
true = ifeq(l0(a),true,p1(a,a,a),true),
inference(reorient_equations,[],[f247]) ).
fof(f343,axiom,
! [X2,X0,X1] : ifeq(p1(X0,X1,X2),true,n2(X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_137) ).
fof(f344,plain,
! [X2,X0,X1] : true = ifeq(p1(X0,X1,X2),true,n2(X2),true),
inference(reorient_equations,[],[f343]) ).
fof(f421,axiom,
! [X0,X1] : ifeq(m1(X0,X1,X0),true,p2(X1,X0,X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_176) ).
fof(f422,plain,
! [X0,X1] : true = ifeq(m1(X0,X1,X0),true,p2(X1,X0,X1),true),
inference(reorient_equations,[],[f421]) ).
fof(f553,axiom,
! [X0] : ifeq(n2(X0),true,p3(X0,X0,X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_244) ).
fof(f554,plain,
! [X0] : true = ifeq(n2(X0),true,p3(X0,X0,X0),true),
inference(reorient_equations,[],[f553]) ).
fof(f599,axiom,
! [X2,X0,X1] : ifeq(p2(X0,X1,X2),true,r3(X0,X2,X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_267) ).
fof(f600,plain,
! [X2,X0,X1] : true = ifeq(p2(X0,X1,X2),true,r3(X0,X2,X0),true),
inference(reorient_equations,[],[f599]) ).
fof(f659,axiom,
! [X2,X3,X0,X1] : ifeq(p3(X0,X1,X2),true,ifeq(l1(X3,X1),true,s4(X3),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_299) ).
fof(f660,plain,
! [X2,X3,X0,X1] : true = ifeq(p3(X0,X1,X2),true,ifeq(l1(X3,X1),true,s4(X3),true),true),
inference(reorient_equations,[],[f659]) ).
fof(f661,axiom,
! [X2,X0,X1] : ifeq(s4(X0),true,ifeq(r3(X1,X2,X2),true,k5(X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_300) ).
fof(f662,plain,
! [X2,X0,X1] : true = ifeq(s4(X0),true,ifeq(r3(X1,X2,X2),true,k5(X2),true),true),
inference(reorient_equations,[],[f661]) ).
fof(f723,negated_conjecture,
k5(b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f724,plain,
true != k5(b),
inference(reorient_equations,[],[f723]) ).
fof(f768,plain,
true = ifeq(true,true,l1(a,a),true),
inference(superposition,[],[f80,f74]) ).
fof(f771,plain,
true = l1(a,a),
inference(forward_demodulation,[],[f768,f1]) ).
fof(f820,plain,
true = ifeq(true,true,p1(a,a,a),true),
inference(forward_demodulation,[],[f248,f40]) ).
fof(f821,plain,
true = p1(a,a,a),
inference(forward_demodulation,[],[f820,f1]) ).
fof(f846,plain,
true = ifeq(true,true,n2(a),true),
inference(superposition,[],[f344,f821]) ).
fof(f847,plain,
true = n2(a),
inference(forward_demodulation,[],[f846,f1]) ).
fof(f923,plain,
true = ifeq(true,true,p3(a,a,a),true),
inference(superposition,[],[f554,f847]) ).
fof(f928,plain,
true = p3(a,a,a),
inference(forward_demodulation,[],[f923,f1]) ).
fof(f1386,plain,
true = ifeq(true,true,m1(e,b,e),true),
inference(superposition,[],[f86,f62]) ).
fof(f1392,plain,
true = m1(e,b,e),
inference(forward_demodulation,[],[f1386,f1]) ).
fof(f1607,plain,
true = ifeq(true,true,p2(b,e,b),true),
inference(superposition,[],[f422,f1392]) ).
fof(f1620,plain,
true = p2(b,e,b),
inference(forward_demodulation,[],[f1607,f1]) ).
fof(f1680,plain,
true = ifeq(true,true,r3(b,b,b),true),
inference(superposition,[],[f600,f1620]) ).
fof(f1683,plain,
true = r3(b,b,b),
inference(forward_demodulation,[],[f1680,f1]) ).
fof(f2291,plain,
! [X0] : true = ifeq(s4(X0),true,ifeq(true,true,k5(b),true),true),
inference(superposition,[],[f662,f1683]) ).
fof(f2294,plain,
! [X0] : true = ifeq(s4(X0),true,k5(b),true),
inference(forward_demodulation,[],[f2291,f1]) ).
fof(f2941,plain,
! [X0] : true = ifeq(true,true,ifeq(l1(X0,a),true,s4(X0),true),true),
inference(superposition,[],[f660,f928]) ).
fof(f2956,plain,
! [X0] : true = ifeq(l1(X0,a),true,s4(X0),true),
inference(forward_demodulation,[],[f2941,f1]) ).
fof(f2960,plain,
true = ifeq(true,true,s4(a),true),
inference(superposition,[],[f2956,f771]) ).
fof(f2962,plain,
true = s4(a),
inference(forward_demodulation,[],[f2960,f1]) ).
fof(f2975,plain,
true = ifeq(true,true,k5(b),true),
inference(superposition,[],[f2294,f2962]) ).
fof(f2985,plain,
true = k5(b),
inference(forward_demodulation,[],[f2975,f1]) ).
fof(f2996,plain,
$false,
inference(forward_subsumption_resolution,[],[f2985,f724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN116-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:34:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 4.18/1.37 % (1856590)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.18/1.37 % (1856595)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=2552134242:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.18/1.37 % (1856599)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3058404880:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.18/1.37 % (1856596)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=2038472878:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.18/1.37 % (1856597)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3802012214:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.18/1.37 % (1856598)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3352826145:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.18/1.37 % (1856601)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2310881362:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.18/1.37 % (1856600)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1722613652:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.18/1.37 % (1856599)Refutation not found, incomplete strategy
% 4.18/1.37 % (1856599)------------------------------
% 4.18/1.37 % (1856599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.37 % (1856599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.37 % (1856599)CaDiCaL version: 2.1.3
% 4.18/1.37 % (1856599)Termination reason: Refutation not found, incomplete strategy
% 4.18/1.37 % (1856599)Time elapsed: 0.037 s
% 4.18/1.37 % (1856599)Peak memory usage: 89 MB
% 4.18/1.37 % (1856599)Instructions burned: 68 (million)
% 4.18/1.37 % (1856598)Instruction limit reached!
% 4.18/1.37 % (1856598)------------------------------
% 4.18/1.37 % (1856598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.37 % (1856598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.37 % (1856598)CaDiCaL version: 2.1.3
% 4.18/1.37 % (1856598)Termination reason: Instruction limit
% 4.18/1.37 % (1856598)Termination phase: Saturation
% 4.18/1.37 % (1856598)Time elapsed: 0.075 s
% 4.18/1.37 % (1856598)Peak memory usage: 88 MB
% 4.18/1.37 % (1856598)Instructions burned: 137 (million)
% 4.18/1.37 % (1856601)First to succeed.
% 4.18/1.37 % (1856601)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1856590"
% 4.18/1.37 % (1856600)Instruction limit reached!
% 4.18/1.37 % (1856600)------------------------------
% 4.18/1.37 % (1856600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.37 % (1856600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.37 % (1856600)CaDiCaL version: 2.1.3
% 4.18/1.37 % (1856600)Termination reason: Instruction limit
% 4.18/1.37 % (1856600)Termination phase: Saturation
% 4.18/1.37 % (1856600)Time elapsed: 0.152 s
% 4.18/1.37 % (1856600)Peak memory usage: 91 MB
% 4.18/1.37 % (1856600)Instructions burned: 258 (million)
% 4.18/1.37 % (1856609)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2143574674:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.18/1.37 % (1856599)------------------------------
% 4.18/1.37 % (1856599)------------------------------
% 4.18/1.37 % (1856601)Refutation found. Thanks to Tanya!
% 4.18/1.37 % SZS status Unsatisfiable for theBenchmark
% 4.18/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.18/1.37 % (1856601)------------------------------
% 4.18/1.37 % (1856601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.37 % (1856601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.37 % (1856601)CaDiCaL version: 2.1.3
% 4.18/1.37 % (1856601)Termination reason: Refutation
% 4.18/1.37 % (1856601)Time elapsed: 0.068 s
% 4.18/1.37 % (1856601)Peak memory usage: 89 MB
% 4.18/1.37 % (1856601)Instructions burned: 118 (million)
% 4.18/1.37 % (1856601)------------------------------
% 4.18/1.37 % (1856601)------------------------------
% 4.18/1.37 % (1856590)Success in time 0.515 s
% 4.18/1.37 % Vampire exiting
%------------------------------------------------------------------------------