%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG023-7 : 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 : n019.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 12:35:09 PM UTC 2026
% Result : Unsatisfiable 2.74s 1.35s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
fof(f17,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
fof(f18,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
fof(f20,axiom,
! [X0,X1] : multiply(additive_inverse(X0),additive_inverse(X1)) = multiply(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_of_inverses) ).
fof(f21,plain,
! [X0,X1] : multiply(X0,X1) = multiply(additive_inverse(X0),additive_inverse(X1)),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
fof(f23,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
fof(f25,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(reorient_equations,[],[f24]) ).
fof(f30,negated_conjecture,
associator(x,x,y) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_alternative) ).
fof(f31,plain,
additive_identity != associator(x,x,y),
inference(reorient_equations,[],[f30]) ).
fof(f53,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(superposition,[],[f21,f11]) ).
fof(f79,plain,
! [X0,X1] : additive_identity = add(multiply(X0,X1),multiply(X0,additive_inverse(X1))),
inference(superposition,[],[f10,f25]) ).
fof(f1903,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(additive_inverse(X0),multiply(X1,X2))),
inference(forward_demodulation,[],[f18,f23]) ).
fof(f1904,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(X0,additive_inverse(multiply(X1,X2)))),
inference(forward_demodulation,[],[f1903,f53]) ).
fof(f1905,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(additive_inverse(X1),X2))),
inference(forward_demodulation,[],[f1904,f23]) ).
fof(f1906,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,additive_inverse(X2)))),
inference(forward_demodulation,[],[f1905,f53]) ).
fof(f2087,plain,
! [X0,X1] : add(multiply(X0,multiply(X0,X1)),multiply(X0,multiply(X0,additive_inverse(X1)))) = associator(X0,X0,X1),
inference(superposition,[],[f1906,f17]) ).
fof(f2151,plain,
! [X0,X1] : associator(X0,X0,X1) = multiply(X0,add(multiply(X0,X1),multiply(X0,additive_inverse(X1)))),
inference(forward_demodulation,[],[f2087,f12]) ).
fof(f2170,plain,
! [X0,X1] : multiply(X0,additive_identity) = associator(X0,X0,X1),
inference(forward_demodulation,[],[f2151,f79]) ).
fof(f2185,plain,
! [X0,X1] : additive_identity = associator(X0,X0,X1),
inference(forward_demodulation,[],[f2170,f6]) ).
fof(f2201,plain,
additive_identity != additive_identity,
inference(superposition,[],[f31,f2185]) ).
fof(f2202,plain,
$false,
inference(trivial_inequality_removal,[],[f2201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG023-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:59:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.74/1.35 % (3504621)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.74/1.35 % (3504632)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1910382148:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.74/1.35 % (3504632)First to succeed.
% 2.74/1.35 % (3504632)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3504621"
% 2.74/1.35 % (3504631)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1754809711:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.74/1.35 % (3504629)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3578016340:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.74/1.35 % (3504627)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=4074397471:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.74/1.35 % (3504628)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3703594958:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.74/1.35 % (3504626)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=1457447752:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.74/1.35 % (3504630)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1506599843:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.74/1.35 % (3504630)Refutation not found, incomplete strategy
% 2.74/1.35 % (3504630)------------------------------
% 2.74/1.35 % (3504630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.35 % (3504630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.35 % (3504630)CaDiCaL version: 2.1.3
% 2.74/1.35 % (3504630)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.35 % (3504630)Time elapsed: 0.002 s
% 2.74/1.35 % (3504629)Also succeeded, but the first one will report.
% 2.74/1.35 % (3504630)Peak memory usage: 87 MB
% 2.74/1.35 % (3504630)Instructions burned: 1 (million)
% 2.74/1.35 % (3504631)Also succeeded, but the first one will report.
% 2.74/1.35 % (3504632)Refutation found. Thanks to Tanya!
% 2.74/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.35 % (3504632)------------------------------
% 2.74/1.35 % (3504632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.35 % (3504632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.35 % (3504632)CaDiCaL version: 2.1.3
% 2.74/1.35 % (3504632)Termination reason: Refutation
% 2.74/1.35 % (3504632)Time elapsed: 0.020 s
% 2.74/1.35 % (3504632)Peak memory usage: 88 MB
% 2.74/1.35 % (3504632)Instructions burned: 65 (million)
% 2.74/1.35 % (3504632)------------------------------
% 2.74/1.35 % (3504632)------------------------------
% 2.74/1.35 % (3504621)Success in time 0.305 s
% 2.74/1.35 % Vampire exiting
%------------------------------------------------------------------------------