%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG019-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:35:44 PM UTC 2026
% Result : Unsatisfiable 0.30s 0.67s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',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/sandbox2/benchmark/Axioms/RNG003-0.ax',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/sandbox2/benchmark/Axioms/RNG003-0.ax',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/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
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/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).
fof(f20,negated_conjecture,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form1) ).
fof(f21,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))),
inference(definition_unfolding,[],[f20,f18,f18,f18]) ).
fof(f29,plain,
! [X0,X1] : add(add(X0,additive_inverse(X0)),X1) = X1,
inference(superposition,[],[f1,f10]) ).
fof(f31,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f29,f15]) ).
fof(f50,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f57,plain,
! [X0,X1] : additive_identity = add(X0,add(X1,additive_inverse(add(X0,X1)))),
inference(superposition,[],[f10,f15]) ).
fof(f59,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f94,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(superposition,[],[f31,f11]) ).
fof(f158,plain,
! [X0,X1] : multiply(X0,additive_identity) = add(multiply(X0,X1),multiply(X0,additive_inverse(X1))),
inference(superposition,[],[f12,f10]) ).
fof(f471,plain,
! [X0,X1] : add(X1,additive_inverse(add(X0,X1))) = add(additive_inverse(X0),additive_identity),
inference(superposition,[],[f94,f57]) ).
fof(f480,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(forward_demodulation,[],[f471,f2]) ).
fof(f601,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f50]) ).
fof(f952,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
inference(superposition,[],[f94,f480]) ).
fof(f1053,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(additive_inverse(multiply(X0,X1)),multiply(X0,additive_identity)),
inference(superposition,[],[f94,f158]) ).
fof(f1056,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = add(additive_inverse(multiply(X0,X1)),additive_identity),
inference(forward_demodulation,[],[f1053,f6]) ).
fof(f1092,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f1056,f2]) ).
fof(f1821,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,additive_inverse(multiply(y,add(u,v))))),
inference(superposition,[],[f21,f1092]) ).
fof(f1848,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
inference(forward_demodulation,[],[f1821,f1092]) ).
fof(f1862,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,add(additive_inverse(v),additive_inverse(u))))),
inference(forward_demodulation,[],[f1848,f952]) ).
fof(f1872,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,add(multiply(y,additive_inverse(v)),multiply(y,additive_inverse(u))))),
inference(forward_demodulation,[],[f1862,f12]) ).
fof(f1878,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(multiply(x,y),add(u,v)),add(multiply(x,multiply(y,additive_inverse(v))),multiply(x,multiply(y,additive_inverse(u))))),
inference(forward_demodulation,[],[f1872,f12]) ).
fof(f1883,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(v))))),
inference(forward_demodulation,[],[f1878,f59]) ).
fof(f1886,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(x,multiply(y,additive_inverse(u))),add(add(multiply(multiply(x,y),u),multiply(multiply(x,y),v)),multiply(x,multiply(y,additive_inverse(v))))),
inference(forward_demodulation,[],[f1883,f12]) ).
fof(f1889,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))),
inference(forward_demodulation,[],[f1886,f15]) ).
fof(f1891,plain,
add(add(multiply(multiply(x,y),u),additive_inverse(multiply(x,multiply(y,u)))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v))))) != add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))),
inference(forward_demodulation,[],[f1889,f601]) ).
fof(f1892,plain,
add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))) != add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))),
inference(forward_demodulation,[],[f1891,f15]) ).
fof(f1893,plain,
add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))) != add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),multiply(x,additive_inverse(multiply(y,v)))))),
inference(forward_demodulation,[],[f1892,f1092]) ).
fof(f1894,plain,
add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))) != add(multiply(multiply(x,y),u),add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))),
inference(forward_demodulation,[],[f1893,f1092]) ).
fof(f1895,plain,
add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))) != add(multiply(multiply(x,y),u),add(multiply(x,additive_inverse(multiply(y,u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))),
inference(forward_demodulation,[],[f1894,f1092]) ).
fof(f1896,plain,
add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))) != add(multiply(multiply(x,y),u),add(multiply(x,multiply(y,additive_inverse(u))),add(multiply(multiply(x,y),v),multiply(x,multiply(y,additive_inverse(v)))))),
inference(forward_demodulation,[],[f1895,f1092]) ).
fof(f1897,plain,
$false,
inference(trivial_inequality_removal,[],[f1896]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG019-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.48 % Computer : n008.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.49 % CPULimit : 300
% 0.21/0.49 % WCLimit : 300
% 0.21/0.49 % DateTime : Sun Sep 27 22:59:24 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.54 Running first-order model finding
% 0.26/0.54 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.67 % (1707075)Will run a generic schedule for satisfiability detection.
% 0.30/0.67 % (1707086)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1316899392:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.30/0.67 % (1707081)% WARNING: option uhcvi not known.
% 0.30/0.67 % (1707083)dis+10_1_sil=32000:sp=arity:random_seed=470803497:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.30/0.67 % (1707080)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3689862770_2999 on theBenchmark for (2999ds/0Mi)
% 0.30/0.67 % (1707085)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1897528628:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.30/0.67 % (1707082)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2643087519:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.30/0.67 % (1707081)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3473937572:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.30/0.67 % (1707084)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1445129319:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.30/0.67 % TRYING [1]
% 0.30/0.67 % TRYING [2]
% 0.30/0.67 % TRYING [3]
% 0.30/0.67 % TRYING [4]
% 0.30/0.67 % (1707085) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1707075-1707085"...
% 0.30/0.67 % (1707084) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1707075-1707084"...
% 0.30/0.67 % (1707085)...printing done.
% 0.30/0.67 % (1707084)...printing done.
% 0.30/0.67 % (1707085)Refutation found. Thanks to Tanya!
% 0.30/0.67 % SZS status Unsatisfiable for theBenchmark
% 0.30/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/0.67 % (1707085)------------------------------
% 0.30/0.67 % (1707085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.67 % (1707085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.67 % (1707085)CaDiCaL version: 2.1.3
% 0.30/0.67 % (1707085)Termination reason: Refutation
% 0.30/0.67 % (1707085)Time elapsed: 0.060 s
% 0.30/0.67 % (1707085)Peak memory usage: 12 MB
% 0.30/0.67 % (1707085)Instructions burned: 59 (million)
% 0.30/0.67 % (1707075)Success in time 0.117 s
% 0.30/0.67 % Vampire exiting
%------------------------------------------------------------------------------