%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ROB023-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:36:17 PM UTC 2026
% Result : Unsatisfiable 3.18s 1.33s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 59 unt; 1 def)
% Number of atoms : 69 ( 57 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 4 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f2,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
fof(f3,axiom,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
fof(f4,axiom,
! [X0] : add(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_x_is_x) ).
fof(f5,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
fof(f6,plain,
b != add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),
inference(reorient_equations,[],[f5]) ).
fof(f8,definition,
( spl0_1
<=> b = add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
( b != add(negate(add(a,negate(b))),negate(add(negate(a),negate(b))))
| spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f11,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f6,f8]) ).
fof(f12,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(X0,X1)),
inference(superposition,[],[f2,f4]) ).
fof(f14,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f21,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f23,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(forward_demodulation,[],[f14,f2]) ).
fof(f28,plain,
! [X0,X1] : add(X0,X1) = add(X1,add(X0,X1)),
inference(superposition,[],[f12,f1]) ).
fof(f52,plain,
! [X0] : negate(add(negate(X0),negate(add(X0,negate(X0))))) = X0,
inference(superposition,[],[f3,f4]) ).
fof(f54,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X1,negate(X0))))) = X1,
inference(superposition,[],[f3,f1]) ).
fof(f58,plain,
! [X0,X1] : negate(add(X0,X1)) = negate(add(X0,negate(add(negate(add(X0,X1)),negate(negate(add(X0,negate(X1)))))))),
inference(superposition,[],[f3,f3]) ).
fof(f60,plain,
! [X0] : negate(X0) = negate(add(negate(add(negate(X0),X0)),negate(negate(X0)))),
inference(superposition,[],[f3,f4]) ).
fof(f70,plain,
! [X0] : negate(X0) = negate(add(negate(add(negate(X0),add(X0,negate(X0)))),X0)),
inference(superposition,[],[f3,f52]) ).
fof(f73,plain,
! [X0] : negate(X0) = negate(add(negate(add(X0,negate(X0))),X0)),
inference(forward_demodulation,[],[f70,f28]) ).
fof(f273,plain,
! [X0] : negate(add(negate(add(X0,add(negate(X0),negate(add(X0,negate(X0)))))),negate(X0))) = X0,
inference(superposition,[],[f60,f52]) ).
fof(f288,plain,
! [X0] : negate(X0) = negate(add(X0,negate(add(X0,negate(X0))))),
inference(superposition,[],[f73,f1]) ).
fof(f294,plain,
! [X0] : negate(add(X0,negate(X0))) = negate(add(negate(X0),negate(add(negate(add(X0,negate(X0))),negate(X0))))),
inference(superposition,[],[f3,f73]) ).
fof(f635,plain,
! [X0,X1] : negate(add(X1,X0)) = negate(add(X0,negate(add(negate(add(X1,X0)),negate(negate(add(X0,negate(X1)))))))),
inference(superposition,[],[f3,f54]) ).
fof(f670,plain,
! [X0] : negate(add(negate(add(X0,add(X0,negate(X0)))),negate(X0))) = X0,
inference(superposition,[],[f3,f288]) ).
fof(f674,plain,
! [X0] : negate(X0) = negate(add(negate(add(add(X0,negate(add(X0,negate(X0)))),negate(X0))),add(X0,negate(add(X0,negate(X0)))))),
inference(superposition,[],[f73,f288]) ).
fof(f679,plain,
! [X0] : negate(X0) = negate(add(negate(add(X0,add(negate(add(X0,negate(X0))),negate(X0)))),add(X0,negate(add(X0,negate(X0)))))),
inference(forward_demodulation,[],[f674,f2]) ).
fof(f681,plain,
! [X0] : negate(add(negate(add(X0,negate(X0))),negate(X0))) = X0,
inference(forward_demodulation,[],[f670,f12]) ).
fof(f691,plain,
! [X0] : negate(add(X0,negate(X0))) = negate(add(negate(X0),X0)),
inference(backward_demodulation,[],[f294,f681]) ).
fof(f730,plain,
! [X0,X1] : negate(add(X0,add(negate(add(X1,X0)),X1))) = negate(add(add(X1,X0),negate(add(X1,X0)))),
inference(superposition,[],[f691,f21]) ).
fof(f733,plain,
! [X0,X1] : negate(add(add(X0,X1),negate(add(X0,X1)))) = negate(add(X0,add(negate(add(X0,X1)),X1))),
inference(superposition,[],[f691,f23]) ).
fof(f753,plain,
! [X0,X1] : negate(add(X0,add(X1,negate(add(X0,X1))))) = negate(add(X0,add(negate(add(X0,X1)),X1))),
inference(forward_demodulation,[],[f733,f2]) ).
fof(f755,plain,
! [X0,X1] : negate(add(X0,add(negate(add(X1,X0)),X1))) = negate(add(X1,add(X0,negate(add(X1,X0))))),
inference(forward_demodulation,[],[f730,f2]) ).
fof(f765,plain,
! [X0] : negate(X0) = negate(add(negate(add(X0,add(negate(X0),negate(add(X0,negate(X0)))))),add(X0,negate(add(X0,negate(X0)))))),
inference(backward_demodulation,[],[f679,f753]) ).
fof(f786,plain,
! [X0] : add(negate(X0),negate(add(X0,negate(X0)))) = negate(add(negate(add(add(negate(X0),negate(add(X0,negate(X0)))),X0)),X0)),
inference(superposition,[],[f681,f52]) ).
fof(f790,plain,
! [X0] : add(X0,negate(add(X0,negate(X0)))) = negate(add(negate(add(add(X0,negate(add(X0,negate(X0)))),negate(X0))),negate(X0))),
inference(superposition,[],[f681,f288]) ).
fof(f807,plain,
! [X0] : add(X0,negate(add(X0,negate(X0)))) = negate(add(negate(add(X0,add(negate(add(X0,negate(X0))),negate(X0)))),negate(X0))),
inference(forward_demodulation,[],[f790,f2]) ).
fof(f811,plain,
! [X0] : add(negate(X0),negate(add(X0,negate(X0)))) = negate(add(negate(add(negate(X0),add(negate(add(X0,negate(X0))),X0))),X0)),
inference(forward_demodulation,[],[f786,f2]) ).
fof(f816,plain,
! [X0] : negate(add(negate(add(X0,add(negate(X0),negate(add(X0,negate(X0)))))),negate(X0))) = add(X0,negate(add(X0,negate(X0)))),
inference(forward_demodulation,[],[f807,f753]) ).
fof(f819,plain,
! [X0] : add(negate(X0),negate(add(X0,negate(X0)))) = negate(add(negate(add(X0,add(negate(X0),negate(add(X0,negate(X0)))))),X0)),
inference(forward_demodulation,[],[f811,f755]) ).
fof(f824,plain,
! [X0] : add(X0,negate(add(X0,negate(X0)))) = X0,
inference(forward_demodulation,[],[f816,f273]) ).
fof(f830,plain,
! [X0] : negate(X0) = negate(add(negate(add(X0,add(negate(X0),negate(add(X0,negate(X0)))))),X0)),
inference(backward_demodulation,[],[f765,f824]) ).
fof(f841,plain,
! [X0] : negate(X0) = add(negate(X0),negate(add(X0,negate(X0)))),
inference(forward_demodulation,[],[f830,f819]) ).
fof(f852,plain,
! [X0] : negate(negate(X0)) = X0,
inference(backward_demodulation,[],[f52,f841]) ).
fof(f885,plain,
! [X0,X1] : negate(add(X1,X0)) = negate(add(X0,negate(add(negate(add(X1,X0)),add(X0,negate(X1)))))),
inference(backward_demodulation,[],[f635,f852]) ).
fof(f886,plain,
! [X0,X1] : negate(add(X0,X1)) = negate(add(X0,negate(add(negate(add(X0,X1)),add(X0,negate(X1)))))),
inference(backward_demodulation,[],[f58,f852]) ).
fof(f926,plain,
! [X0,X1] : add(negate(add(X0,X1)),negate(add(X0,negate(X1)))) = negate(X0),
inference(superposition,[],[f852,f3]) ).
fof(f927,plain,
! [X0,X1] : negate(X0) = add(negate(add(X1,X0)),negate(add(X0,negate(X1)))),
inference(superposition,[],[f852,f54]) ).
fof(f1301,plain,
! [X0,X1] : negate(add(X0,X1)) = negate(add(X0,negate(add(X0,add(negate(add(X0,X1)),negate(X1)))))),
inference(superposition,[],[f886,f23]) ).
fof(f1400,plain,
! [X0,X1] : negate(X0) = add(negate(add(X0,X1)),negate(X0)),
inference(superposition,[],[f12,f926]) ).
fof(f1448,plain,
! [X0,X1] : negate(X1) = add(negate(add(X0,X1)),negate(X1)),
inference(superposition,[],[f1400,f28]) ).
fof(f1476,plain,
! [X2,X0,X1] : add(X2,negate(X0)) = add(negate(add(X0,X1)),add(X2,negate(X0))),
inference(superposition,[],[f23,f1400]) ).
fof(f1485,plain,
! [X0,X1] : negate(add(X1,X0)) = negate(add(X0,negate(add(X0,negate(X1))))),
inference(backward_demodulation,[],[f885,f1476]) ).
fof(f1496,plain,
! [X0,X1] : negate(add(X0,X1)) = negate(add(X0,negate(add(X0,negate(X1))))),
inference(backward_demodulation,[],[f1301,f1448]) ).
fof(f1503,plain,
! [X0,X1] : negate(add(X0,X1)) = negate(add(X1,X0)),
inference(backward_demodulation,[],[f1485,f1496]) ).
fof(f1607,plain,
! [X0,X1] : negate(X1) = add(negate(add(X0,X1)),negate(add(negate(X0),X1))),
inference(superposition,[],[f927,f1503]) ).
fof(f1639,plain,
( b != negate(negate(b))
| spl0_1 ),
inference(backward_demodulation,[],[f10,f1607]) ).
fof(f1665,plain,
( b != b
| spl0_1 ),
inference(forward_demodulation,[],[f1639,f852]) ).
fof(f1666,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f1665]) ).
fof(f1667,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1666]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f11]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1667]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f1695,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:30:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.18/1.33 % (3327056)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.18/1.33 % (3327064)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1305646054:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.18/1.33 % (3327061)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=1488008206:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.18/1.33 % (3327062)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=1881322455:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.18/1.33 % (3327065)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2268147721:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.18/1.33 % (3327063)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1160613058:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.18/1.33 % (3327064)Instruction limit reached!
% 3.18/1.33 % (3327064)------------------------------
% 3.18/1.33 % (3327064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.33 % (3327064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.33 % (3327064)CaDiCaL version: 2.1.3
% 3.18/1.33 % (3327064)Termination reason: Instruction limit
% 3.18/1.33 % (3327064)Termination phase: Saturation
% 3.18/1.33 % (3327064)Time elapsed: 0.045 s
% 3.18/1.33 % (3327064)Peak memory usage: 89 MB
% 3.18/1.33 % (3327064)Instructions burned: 138 (million)
% 3.18/1.33 % (3327066)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=342892534:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.18/1.33 % (3327067)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1320668099:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.18/1.33 % (3327066)First to succeed.
% 3.18/1.33 % (3327066)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3327056"
% 3.18/1.33 % (3327065)Instruction limit reached!
% 3.18/1.33 % (3327065)------------------------------
% 3.18/1.33 % (3327065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.33 % (3327065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.33 % (3327065)CaDiCaL version: 2.1.3
% 3.18/1.33 % (3327065)Termination reason: Instruction limit
% 3.18/1.33 % (3327065)Termination phase: Saturation
% 3.18/1.33 % (3327065)Time elapsed: 0.097 s
% 3.18/1.33 % (3327065)Peak memory usage: 89 MB
% 3.18/1.33 % (3327065)Instructions burned: 183 (million)
% 3.18/1.33 % (3327075)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2381373473:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.18/1.33 % (3327076)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3661118558:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.18/1.33 % (3327066)Refutation found. Thanks to Tanya!
% 3.18/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.18/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.42 % (3327066)------------------------------
% 3.98/1.42 % (3327066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.42 % (3327066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.42 % (3327066)CaDiCaL version: 2.1.3
% 3.98/1.42 % (3327066)Termination reason: Refutation
% 3.98/1.42 % (3327066)Time elapsed: 0.058 s
% 3.98/1.42 % (3327066)Peak memory usage: 89 MB
% 3.98/1.42 % (3327066)Instructions burned: 94 (million)
% 3.98/1.42 % (3327066)------------------------------
% 3.98/1.42 % (3327066)------------------------------
% 3.98/1.42 % (3327056)Success in time 0.484 s
% 3.98/1.42 % Vampire exiting
%------------------------------------------------------------------------------