%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 09:36:01 AM UTC 2026
% Result : Unsatisfiable 9.02s 2.23s
% Output : Refutation 9.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X2)),inverse(add(X0,inverse(add(inverse(X2),inverse(add(X2,X3)))))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dn1) ).
fof(f2,negated_conjecture,
add(b,a) != add(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',huntinton_1) ).
fof(f3,plain,
! [X2,X0,X1,X4,X5] : inverse(add(inverse(add(X0,X4)),inverse(add(inverse(add(inverse(add(X1,X2)),X0)),inverse(add(inverse(X4),inverse(add(X4,X5)))))))) = X4,
inference(superposition,[],[f1,f1]) ).
fof(f4,plain,
! [X2,X3,X0,X1,X4] : inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))) = inverse(add(X0,inverse(add(inverse(add(X1,X2)),inverse(add(inverse(inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3))))))),inverse(add(inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))),X4)))))))),
inference(superposition,[],[f1,f1]) ).
fof(f7,plain,
! [X2,X0,X1] : inverse(X0) = inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X0)),X1)),X0)),X2)),inverse(X0))),X0)),
inference(superposition,[],[f1,f1]) ).
fof(f8,plain,
! [X0] : inverse(X0) = inverse(add(inverse(add(X0,inverse(X0))),X0)),
inference(superposition,[],[f7,f1]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : inverse(add(inverse(X0),inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X0)),X1)),X0)),X2)),inverse(add(inverse(X0),inverse(add(X0,X3)))))))) = X0,
inference(superposition,[],[f1,f7]) ).
fof(f19,plain,
! [X0,X1] : inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X0),inverse(add(X0,X1)))))))) = X0,
inference(superposition,[],[f1,f8]) ).
fof(f34,plain,
! [X2,X0,X1] : inverse(add(inverse(add(inverse(add(X1,X2)),X0)),inverse(add(X1,X0)))) = X0,
inference(superposition,[],[f1,f19]) ).
fof(f64,plain,
! [X2,X0] : inverse(add(inverse(add(X0,X2)),inverse(add(inverse(X0),X2)))) = X2,
inference(superposition,[],[f34,f19]) ).
fof(f106,plain,
! [X0] : inverse(add(inverse(add(add(X0,inverse(X0)),X0)),inverse(X0))) = X0,
inference(superposition,[],[f64,f8]) ).
fof(f167,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X0)),inverse(add(X0,X1)))) = X0,
inference(superposition,[],[f3,f34]) ).
fof(f198,plain,
! [X0] : inverse(X0) = inverse(add(X0,inverse(add(add(X0,inverse(X0)),inverse(X0))))),
inference(superposition,[],[f34,f106]) ).
fof(f233,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(X0),X1)),inverse(add(X0,X1)))) = X1,
inference(superposition,[],[f34,f198]) ).
fof(f363,plain,
! [X0] : inverse(add(inverse(add(inverse(X0),X0)),inverse(X0))) = X0,
inference(superposition,[],[f3,f167]) ).
fof(f557,plain,
! [X0] : inverse(X0) = inverse(add(X0,inverse(add(inverse(X0),inverse(X0))))),
inference(superposition,[],[f34,f363]) ).
fof(f662,plain,
! [X0] : inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X0),inverse(X0))))))) = X0,
inference(superposition,[],[f19,f557]) ).
fof(f690,plain,
! [X0] : inverse(add(inverse(X0),inverse(X0))) = X0,
inference(forward_demodulation,[],[f662,f557]) ).
fof(f709,plain,
! [X0] : inverse(add(inverse(X0),inverse(X0))) = add(X0,inverse(add(inverse(X0),inverse(X0)))),
inference(superposition,[],[f690,f557]) ).
fof(f753,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f709,f690]) ).
fof(f768,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X0)),inverse(X0))) = X0,
inference(superposition,[],[f34,f753]) ).
fof(f777,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f690,f753]) ).
fof(f795,plain,
! [X0,X1] : inverse(X0) = add(inverse(add(inverse(X1),X0)),inverse(add(X1,X0))),
inference(superposition,[],[f777,f233]) ).
fof(f835,plain,
! [X2,X3,X0,X1,X4] : inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))) = inverse(add(X0,inverse(add(inverse(add(X1,X2)),inverse(add(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3))))),inverse(add(inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,X3)))))),X4)))))))),
inference(forward_demodulation,[],[f4,f777]) ).
fof(f3385,plain,
! [X0,X1] : inverse(add(X0,X1)) = inverse(add(X0,inverse(inverse(add(X0,X1))))),
inference(superposition,[],[f768,f167]) ).
fof(f3387,plain,
! [X0,X1] : inverse(add(X1,X0)) = inverse(add(X0,inverse(inverse(add(X1,X0))))),
inference(superposition,[],[f768,f34]) ).
fof(f3530,plain,
! [X0,X1] : inverse(add(X1,X0)) = inverse(add(X0,add(X1,X0))),
inference(forward_demodulation,[],[f3387,f777]) ).
fof(f3532,plain,
! [X0,X1] : inverse(add(X0,X1)) = inverse(add(X0,add(X0,X1))),
inference(forward_demodulation,[],[f3385,f777]) ).
fof(f4544,plain,
! [X0,X1] : inverse(inverse(X0)) = inverse(add(inverse(add(X1,X0)),inverse(X0))),
inference(superposition,[],[f3530,f795]) ).
fof(f4551,plain,
! [X0,X1] : inverse(add(inverse(add(X1,X0)),inverse(X0))) = X0,
inference(forward_demodulation,[],[f4544,f777]) ).
fof(f5876,plain,
! [X2,X3,X0,X1] : inverse(add(inverse(X0),inverse(add(inverse(add(inverse(add(inverse(add(X0,X1)),X0)),X2)),inverse(add(inverse(X0),inverse(add(X0,X3)))))))) = X0,
inference(forward_demodulation,[],[f11,f777]) ).
fof(f6068,plain,
! [X0,X1] : inverse(add(inverse(X0),add(inverse(X0),inverse(add(X0,X1))))) = X0,
inference(superposition,[],[f5876,f4551]) ).
fof(f6181,plain,
! [X0,X1] : inverse(add(inverse(X0),inverse(add(X0,X1)))) = X0,
inference(forward_demodulation,[],[f6068,f3532]) ).
fof(f6545,plain,
! [X0,X1] : inverse(X0) = add(inverse(X0),inverse(add(X0,X1))),
inference(superposition,[],[f777,f6181]) ).
fof(f7072,plain,
! [X0,X1] : add(X0,inverse(add(inverse(X0),X1))) = X0,
inference(superposition,[],[f6545,f777]) ).
fof(f7484,plain,
! [X2,X0,X1,X4] : inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))) = inverse(add(X1,inverse(add(inverse(X0),inverse(add(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2))))),inverse(add(inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))),X4)))))))),
inference(superposition,[],[f835,f7072]) ).
fof(f7535,plain,
! [X2,X0,X1] : inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))) = inverse(add(X1,inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))))))),
inference(forward_demodulation,[],[f7484,f7072]) ).
fof(f7613,plain,
! [X2,X0,X1] : inverse(add(X0,inverse(add(inverse(X1),inverse(add(X1,X2)))))) = inverse(add(X1,X0)),
inference(forward_demodulation,[],[f7535,f6181]) ).
fof(f7623,plain,
! [X0,X1] : inverse(add(X0,X1)) = inverse(add(X1,X0)),
inference(forward_demodulation,[],[f7613,f6181]) ).
fof(f8609,plain,
! [X0,X1] : add(X1,X0) = inverse(inverse(add(X0,X1))),
inference(superposition,[],[f777,f7623]) ).
fof(f8640,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[],[f8609,f777]) ).
fof(f9161,plain,
add(b,a) != add(b,a),
inference(superposition,[],[f2,f8640]) ).
fof(f9162,plain,
$false,
inference(trivial_inequality_removal,[],[f9161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n007.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Mon Sep 28 21:06:10 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.31/0.34 Running first-order theorem proving
% 0.31/0.34 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
% 6.58/1.89 % (2826842)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.58/1.89 % (2826852)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1663114657:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.58/1.89 % (2826851)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4221014709:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.58/1.89 % (2826850)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1507622662:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.58/1.89 % (2826853)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1456969583:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.58/1.89 % (2826849)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=899331729:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.58/1.89 % (2826848)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=4155173606:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.58/1.89 % (2826847)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=689436909:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.58/1.89 % (2826852)Instruction limit reached!
% 6.58/1.89 % (2826852)------------------------------
% 6.58/1.89 % (2826852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.89 % (2826852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.89 % (2826852)CaDiCaL version: 2.1.3
% 6.58/1.89 % (2826852)Termination reason: Instruction limit
% 6.58/1.89 % (2826852)Termination phase: Saturation
% 6.58/1.89 % (2826852)Time elapsed: 0.133 s
% 6.58/1.89 % (2826852)Peak memory usage: 91 MB
% 6.58/1.89 % (2826852)Instructions burned: 257 (million)
% 6.58/1.89 % (2826850)Instruction limit reached!
% 6.58/1.89 % (2826850)------------------------------
% 6.58/1.89 % (2826850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.89 % (2826850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.89 % (2826850)CaDiCaL version: 2.1.3
% 6.58/1.89 % (2826850)Termination reason: Instruction limit
% 6.58/1.89 % (2826850)Termination phase: Saturation
% 6.58/1.89 % (2826850)Time elapsed: 0.134 s
% 6.58/1.89 % (2826850)Peak memory usage: 89 MB
% 6.58/1.89 % (2826850)Instructions burned: 137 (million)
% 6.58/1.89 % (2826851)Instruction limit reached!
% 6.58/1.89 % (2826851)------------------------------
% 6.58/1.89 % (2826851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.89 % (2826851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.89 % (2826851)CaDiCaL version: 2.1.3
% 6.58/1.89 % (2826851)Termination reason: Instruction limit
% 6.58/1.89 % (2826851)Termination phase: Saturation
% 6.58/1.89 % (2826851)Time elapsed: 0.162 s
% 6.58/1.89 % (2826851)Peak memory usage: 89 MB
% 6.58/1.89 % (2826851)Instructions burned: 181 (million)
% 6.58/1.89 % (2826861)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2290527862:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 6.58/1.89 % (2826862)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1556107680:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 6.58/1.89 % (2826863)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2755237418:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 6.58/1.89 % (2826853)First to succeed.
% 6.58/1.89 % (2826853)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2826842"
% 6.58/1.89 % (2826863)Instruction limit reached!
% 6.58/1.89 % (2826863)------------------------------
% 6.58/1.89 % (2826863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.58/1.89 % (2826863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.58/1.89 % (2826863)CaDiCaL version: 2.1.3
% 9.02/2.23 % (2826863)Termination reason: Instruction limit
% 9.02/2.23 % (2826863)Termination phase: Saturation
% 9.02/2.23 % (2826863)Time elapsed: 0.150 s
% 9.02/2.23 % (2826863)Peak memory usage: 102 MB
% 9.02/2.23 % (2826863)Instructions burned: 216 (million)
% 9.02/2.23 % (2826853)Refutation found. Thanks to Tanya!
% 9.02/2.23 % SZS status Unsatisfiable for theBenchmark
% 9.02/2.23 % SZS output start Proof for theBenchmark
% See solution above
% 9.02/2.23 % (2826853)------------------------------
% 9.02/2.23 % (2826853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.02/2.23 % (2826853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.02/2.23 % (2826853)CaDiCaL version: 2.1.3
% 9.02/2.23 % (2826853)Termination reason: Refutation
% 9.02/2.23 % (2826853)Time elapsed: 0.478 s
% 9.02/2.23 % (2826853)Peak memory usage: 93 MB
% 9.02/2.23 % (2826853)Instructions burned: 541 (million)
% 9.02/2.23 % (2826853)------------------------------
% 9.02/2.23 % (2826853)------------------------------
% 9.02/2.23 % (2826842)Success in time 1.156 s
% 9.02/2.23 % Vampire exiting
%------------------------------------------------------------------------------