%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG021-7 : 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 : 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 12:35:45 PM UTC 2026
% Result : Unsatisfiable 0.38s 0.47s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).
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(f24,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/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(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_linearised_form3) ).
fof(f31,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(add(multiply(multiply(u,x),y),additive_inverse(multiply(u,multiply(x,y)))),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y))))),
inference(definition_unfolding,[],[f30,f18,f18,f18]) ).
fof(f98,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f108,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f303,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X2),add(multiply(X1,X2),X3)) = add(multiply(add(X0,X1),X2),X3),
inference(superposition,[],[f15,f13]) ).
fof(f1108,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(multiply(u,x),y),add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y)))))),
inference(superposition,[],[f31,f98]) ).
fof(f1144,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(multiply(u,x),y),add(add(multiply(multiply(v,x),y),additive_inverse(multiply(v,multiply(x,y)))),additive_inverse(multiply(u,multiply(x,y))))),
inference(forward_demodulation,[],[f1108,f108]) ).
fof(f1174,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(multiply(u,x),y),add(multiply(multiply(v,x),y),add(additive_inverse(multiply(v,multiply(x,y))),additive_inverse(multiply(u,multiply(x,y)))))),
inference(forward_demodulation,[],[f1144,f15]) ).
fof(f1187,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(add(multiply(u,x),multiply(v,x)),y),add(additive_inverse(multiply(v,multiply(x,y))),additive_inverse(multiply(u,multiply(x,y))))),
inference(forward_demodulation,[],[f1174,f303]) ).
fof(f1193,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(add(multiply(u,x),multiply(v,x)),y),additive_inverse(multiply(v,multiply(x,y))))),
inference(forward_demodulation,[],[f1187,f108]) ).
fof(f1197,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),multiply(add(multiply(u,x),multiply(v,x)),y))),
inference(forward_demodulation,[],[f1193,f14]) ).
fof(f1199,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(additive_inverse(multiply(v,multiply(x,y))),multiply(multiply(add(u,v),x),y))),
inference(forward_demodulation,[],[f1197,f13]) ).
fof(f1200,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(additive_inverse(multiply(u,multiply(x,y))),add(multiply(v,additive_inverse(multiply(x,y))),multiply(multiply(add(u,v),x),y))),
inference(forward_demodulation,[],[f1199,f25]) ).
fof(f1201,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(v,additive_inverse(multiply(x,y))),add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(u,multiply(x,y))))),
inference(forward_demodulation,[],[f1200,f108]) ).
fof(f1202,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(v,additive_inverse(multiply(x,y))),add(additive_inverse(multiply(u,multiply(x,y))),multiply(multiply(add(u,v),x),y))),
inference(forward_demodulation,[],[f1201,f14]) ).
fof(f1203,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(v,additive_inverse(multiply(x,y))),add(multiply(u,additive_inverse(multiply(x,y))),multiply(multiply(add(u,v),x),y))),
inference(forward_demodulation,[],[f1202,f25]) ).
fof(f1204,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(add(v,u),additive_inverse(multiply(x,y))),multiply(multiply(add(u,v),x),y)),
inference(forward_demodulation,[],[f1203,f303]) ).
fof(f1205,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(multiply(add(u,v),x),y),multiply(add(v,u),additive_inverse(multiply(x,y)))),
inference(forward_demodulation,[],[f1204,f14]) ).
fof(f1206,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(multiply(add(u,v),x),y),multiply(add(v,u),multiply(x,additive_inverse(y)))),
inference(forward_demodulation,[],[f1205,f25]) ).
fof(f1207,plain,
add(multiply(multiply(add(u,v),x),y),additive_inverse(multiply(add(u,v),multiply(x,y)))) != add(multiply(multiply(add(u,v),x),y),multiply(add(u,v),multiply(x,additive_inverse(y)))),
inference(forward_demodulation,[],[f1206,f14]) ).
fof(f1208,plain,
add(multiply(multiply(add(u,v),x),y),multiply(add(u,v),additive_inverse(multiply(x,y)))) != add(multiply(multiply(add(u,v),x),y),multiply(add(u,v),multiply(x,additive_inverse(y)))),
inference(forward_demodulation,[],[f1207,f25]) ).
fof(f1209,plain,
add(multiply(multiply(add(u,v),x),y),multiply(add(u,v),multiply(x,additive_inverse(y)))) != add(multiply(multiply(add(u,v),x),y),multiply(add(u,v),multiply(x,additive_inverse(y)))),
inference(forward_demodulation,[],[f1208,f25]) ).
fof(f1210,plain,
$false,
inference(trivial_inequality_removal,[],[f1209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG021-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 22:57:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.38/0.47 % (1871998)Will run a generic schedule for satisfiability detection.
% 0.38/0.47 % (1872008)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=902889730:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.47 % (1872004)% WARNING: option uhcvi not known.
% 0.38/0.47 % (1872003)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1060022968_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.47 % (1872005)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1836801475:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.47 % (1872006)dis+10_1_sil=32000:sp=arity:random_seed=1371452608:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.47 % (1872007)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2234797872:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.47 % (1872009)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2762780616:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.47 % TRYING [1]
% 0.38/0.47 % TRYING [2]
% 0.38/0.47 % (1872004)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2509141716:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.47 % TRYING [3]
% 0.38/0.47 % (1872007) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1871998-1872007"...
% 0.38/0.47 % TRYING [4]
% 0.38/0.47 % (1872007)...printing done.
% 0.38/0.47 % (1872007)Refutation found. Thanks to Tanya!
% 0.38/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.38/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.47 % (1872007)------------------------------
% 0.38/0.47 % (1872007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.47 % (1872007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.47 % (1872007)CaDiCaL version: 2.1.3
% 0.38/0.47 % (1872007)Termination reason: Refutation
% 0.38/0.47 % (1872007)Time elapsed: 0.023 s
% 0.38/0.47 % (1872007)Peak memory usage: 12 MB
% 0.38/0.47 % (1872007)Instructions burned: 38 (million)
% 0.38/0.47 % (1871998)Success in time 0.058 s
% 0.38/0.47 % Vampire exiting
%------------------------------------------------------------------------------