%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:26:53 PM UTC 2026
% Result : Unsatisfiable 4.72s 1.65s
% Output : Refutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 54 unt; 1 def)
% Number of atoms : 54 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 24 ( 24 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_comm) ).
fof(f2,axiom,
! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_assoc) ).
fof(f3,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_comm) ).
fof(f8,axiom,
! [X0] : times(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
fof(f9,axiom,
! [X2,X0,X1] : times(X0,'+'(X1,X2)) = '+'(times(X0,X1),times(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr) ).
fof(f10,axiom,
! [X2,X0,X1] : times('+'(X0,X1),X2) = '+'(times(X0,X2),times(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr_001) ).
fof(f12,axiom,
! [X0,X1] : times(s(X0),X1) = '+'(X1,times(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_s) ).
fof(f15,axiom,
! [X0] : sum(s(X0)) = '+'(s(X0),sum(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_s) ).
fof(f18,axiom,
! [X0] : cubes(s(X0)) = '+'(times(s(X0),times(s(X0),s(X0))),cubes(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_s) ).
fof(f19,axiom,
! [X0] : '+'(sum(X0),sum(X0)) = times(X0,s(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_sum) ).
fof(f20,axiom,
times(sum(a),sum(a)) = cubes(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction_hypothesis) ).
fof(f21,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f22,definition,
~ sP0(times(sum(s(a)),sum(s(a)))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f23,plain,
sP0(cubes(s(a))),
inference(inequality_splitting,[],[f21,f22]) ).
fof(f24,plain,
~ sP0(times('+'(s(a),sum(a)),'+'(s(a),sum(a)))),
inference(backward_demodulation,[],[f22,f15]) ).
fof(f25,plain,
! [X0] : cubes(s(X0)) = '+'('+'(times(s(X0),s(X0)),times(X0,times(s(X0),s(X0)))),cubes(X0)),
inference(backward_demodulation,[],[f18,f12]) ).
fof(f26,plain,
~ sP0('+'(times('+'(s(a),sum(a)),s(a)),times('+'(s(a),sum(a)),sum(a)))),
inference(forward_demodulation,[],[f24,f9]) ).
fof(f27,plain,
! [X0] : cubes(s(X0)) = '+'(times(s(X0),s(X0)),'+'(times(X0,times(s(X0),s(X0))),cubes(X0))),
inference(forward_demodulation,[],[f25,f2]) ).
fof(f28,plain,
~ sP0('+'(times('+'(s(a),sum(a)),s(a)),'+'(times(s(a),sum(a)),times(sum(a),sum(a))))),
inference(forward_demodulation,[],[f26,f10]) ).
fof(f29,plain,
! [X0] : cubes(s(X0)) = '+'('+'(s(X0),times(X0,s(X0))),'+'(times(X0,'+'(s(X0),times(X0,s(X0)))),cubes(X0))),
inference(forward_demodulation,[],[f27,f12]) ).
fof(f30,plain,
~ sP0('+'(times('+'(s(a),sum(a)),s(a)),'+'(times(s(a),sum(a)),cubes(a)))),
inference(forward_demodulation,[],[f28,f20]) ).
fof(f31,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(times(X0,s(X0)),'+'(times(X0,'+'(s(X0),times(X0,s(X0)))),cubes(X0)))),
inference(forward_demodulation,[],[f29,f2]) ).
fof(f32,plain,
~ sP0('+'(times('+'(s(a),sum(a)),s(a)),'+'('+'(sum(a),times(a,sum(a))),cubes(a)))),
inference(forward_demodulation,[],[f30,f12]) ).
fof(f33,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(times(X0,s(X0)),'+'('+'(times(X0,s(X0)),times(X0,times(X0,s(X0)))),cubes(X0)))),
inference(forward_demodulation,[],[f31,f9]) ).
fof(f34,plain,
~ sP0('+'(times('+'(s(a),sum(a)),s(a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a))))),
inference(forward_demodulation,[],[f32,f2]) ).
fof(f35,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(times(X0,s(X0)),'+'(times(X0,s(X0)),'+'(times(X0,times(X0,s(X0))),cubes(X0))))),
inference(forward_demodulation,[],[f33,f2]) ).
fof(f36,plain,
~ sP0('+'('+'(times(s(a),s(a)),times(sum(a),s(a))),'+'(sum(a),'+'(times(a,sum(a)),cubes(a))))),
inference(forward_demodulation,[],[f34,f10]) ).
fof(f37,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'('+'(sum(X0),sum(X0)),'+'('+'(sum(X0),sum(X0)),'+'(times(X0,'+'(sum(X0),sum(X0))),cubes(X0))))),
inference(forward_demodulation,[],[f35,f19]) ).
fof(f38,plain,
~ sP0('+'(times(s(a),s(a)),'+'(times(sum(a),s(a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a)))))),
inference(forward_demodulation,[],[f36,f2]) ).
fof(f39,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(sum(X0),'+'(sum(X0),'+'('+'(sum(X0),sum(X0)),'+'(times(X0,'+'(sum(X0),sum(X0))),cubes(X0)))))),
inference(forward_demodulation,[],[f37,f2]) ).
fof(f40,plain,
~ sP0('+'('+'(s(a),times(a,s(a))),'+'(times(sum(a),s(a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a)))))),
inference(forward_demodulation,[],[f38,f12]) ).
fof(f41,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(times(X0,'+'(sum(X0),sum(X0))),cubes(X0))))))),
inference(forward_demodulation,[],[f39,f2]) ).
fof(f42,plain,
~ sP0('+'(s(a),'+'(times(a,s(a)),'+'(times(sum(a),s(a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a))))))),
inference(forward_demodulation,[],[f40,f2]) ).
fof(f43,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'('+'(times(X0,sum(X0)),times(X0,sum(X0))),cubes(X0))))))),
inference(forward_demodulation,[],[f41,f9]) ).
fof(f44,plain,
~ sP0('+'(s(a),'+'('+'(sum(a),sum(a)),'+'(times(sum(a),s(a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a))))))),
inference(forward_demodulation,[],[f42,f19]) ).
fof(f45,plain,
! [X0] : cubes(s(X0)) = '+'(s(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(times(X0,sum(X0)),'+'(times(X0,sum(X0)),cubes(X0)))))))),
inference(forward_demodulation,[],[f43,f2]) ).
fof(f46,plain,
~ sP0('+'(s(a),'+'(sum(a),'+'(sum(a),'+'(times(sum(a),s(a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a)))))))),
inference(forward_demodulation,[],[f44,f2]) ).
fof(f93,plain,
! [X0] : s(X0) = '+'(one,times(X0,one)),
inference(superposition,[],[f8,f12]) ).
fof(f96,plain,
! [X0] : s(X0) = '+'(one,X0),
inference(forward_demodulation,[],[f93,f8]) ).
fof(f105,plain,
! [X0] : cubes('+'(one,X0)) = '+'('+'(one,X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(times(X0,sum(X0)),'+'(times(X0,sum(X0)),cubes(X0)))))))),
inference(backward_demodulation,[],[f45,f96]) ).
fof(f113,plain,
~ sP0('+'('+'(one,a),'+'(sum(a),'+'(sum(a),'+'(times(sum(a),'+'(one,a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a)))))))),
inference(backward_demodulation,[],[f46,f96]) ).
fof(f114,plain,
sP0(cubes('+'(one,a))),
inference(backward_demodulation,[],[f23,f96]) ).
fof(f116,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(times(sum(a),'+'(one,a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a))))))))),
inference(forward_demodulation,[],[f113,f2]) ).
fof(f124,plain,
! [X0] : cubes('+'(one,X0)) = '+'(one,'+'(X0,'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(times(X0,sum(X0)),'+'(times(X0,sum(X0)),cubes(X0))))))))),
inference(forward_demodulation,[],[f105,f2]) ).
fof(f130,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'('+'(times(sum(a),one),times(sum(a),a)),'+'(sum(a),'+'(times(a,sum(a)),cubes(a))))))))),
inference(forward_demodulation,[],[f116,f9]) ).
fof(f140,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(times(sum(a),one),'+'(times(sum(a),a),'+'(sum(a),'+'(times(a,sum(a)),cubes(a)))))))))),
inference(forward_demodulation,[],[f130,f2]) ).
fof(f146,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'(times(sum(a),a),'+'(sum(a),'+'(times(a,sum(a)),cubes(a)))))))))),
inference(forward_demodulation,[],[f140,f8]) ).
fof(f153,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'('+'(sum(a),'+'(times(a,sum(a)),cubes(a))),times(sum(a),a)))))))),
inference(superposition,[],[f146,f1]) ).
fof(f154,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'('+'(times(a,sum(a)),cubes(a)),times(sum(a),a))))))))),
inference(forward_demodulation,[],[f153,f2]) ).
fof(f156,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),'+'(cubes(a),times(sum(a),a)))))))))),
inference(forward_demodulation,[],[f154,f2]) ).
fof(f211,plain,
~ sP0('+'(one,'+'(a,'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'(sum(a),'+'(times(a,sum(a)),'+'(cubes(a),times(a,sum(a))))))))))),
inference(superposition,[],[f156,f3]) ).
fof(f340,plain,
! [X0] : cubes('+'(one,X0)) = '+'(one,'+'(X0,'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(sum(X0),'+'(times(X0,sum(X0)),'+'(cubes(X0),times(X0,sum(X0)))))))))),
inference(superposition,[],[f124,f1]) ).
fof(f353,plain,
~ sP0(cubes('+'(one,a))),
inference(backward_demodulation,[],[f211,f340]) ).
fof(f365,plain,
$false,
inference(forward_subsumption_resolution,[],[f353,f114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n006.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 22:05:41 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 4.72/1.65 % (3366582)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.72/1.65 % (3366589)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=2248270799:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.72/1.65 % (3366595)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2694810560:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.72/1.65 % (3366590)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=2647118608:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.72/1.65 % (3366593)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1458249317:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.72/1.65 % (3366594)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1532145239:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.72/1.65 % (3366592)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2237224433:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.72/1.65 % (3366591)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1305293936:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.72/1.65 % (3366592)First to succeed.
% 4.72/1.65 % (3366592)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3366582"
% 4.72/1.65 % (3366593)Instruction limit reached!
% 4.72/1.65 % (3366593)------------------------------
% 4.72/1.65 % (3366593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.65 % (3366593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.65 % (3366593)CaDiCaL version: 2.1.3
% 4.72/1.65 % (3366593)Termination reason: Instruction limit
% 4.72/1.65 % (3366593)Termination phase: Saturation
% 4.72/1.65 % (3366593)Time elapsed: 0.163 s
% 4.72/1.65 % (3366593)Peak memory usage: 89 MB
% 4.72/1.65 % (3366593)Instructions burned: 182 (million)
% 4.72/1.65 % (3366594)Instruction limit reached!
% 4.72/1.65 % (3366594)------------------------------
% 4.72/1.65 % (3366594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.65 % (3366594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.65 % (3366594)CaDiCaL version: 2.1.3
% 4.72/1.65 % (3366594)Termination reason: Instruction limit
% 4.72/1.65 % (3366594)Termination phase: Saturation
% 4.72/1.65 % (3366594)Time elapsed: 0.236 s
% 4.72/1.65 % (3366594)Peak memory usage: 90 MB
% 4.72/1.65 % (3366594)Instructions burned: 258 (million)
% 4.72/1.65 % (3366605)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3314409999:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 4.72/1.65 % (3366592)Refutation found. Thanks to Tanya!
% 4.72/1.65 % SZS status Unsatisfiable for theBenchmark
% 4.72/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 5.66/1.98 % (3366592)------------------------------
% 5.66/1.98 % (3366592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.98 % (3366592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.98 % (3366592)CaDiCaL version: 2.1.3
% 5.66/1.98 % (3366592)Termination reason: Refutation
% 5.66/1.98 % (3366592)Time elapsed: 0.023 s
% 5.66/1.98 % (3366592)Peak memory usage: 87 MB
% 5.66/1.98 % (3366592)Instructions burned: 22 (million)
% 5.66/1.98 % (3366592)------------------------------
% 5.66/1.98 % (3366592)------------------------------
% 5.66/1.98 % (3366582)Success in time 0.687 s
% 5.66/1.98 % Vampire exiting
%------------------------------------------------------------------------------