%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG020-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.21s 0.56s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
fof(f20,negated_conjecture,
associator(x,add(u,v),y) != add(associator(x,u,y),associator(x,v,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_linearised_form2) ).
fof(f21,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(add(multiply(multiply(x,u),y),additive_inverse(multiply(x,multiply(u,y)))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y))))),
inference(definition_unfolding,[],[f20,f18,f18,f18]) ).
fof(f39,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f15,f10]) ).
fof(f47,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,u),y),add(additive_inverse(multiply(x,multiply(u,y))),add(multiply(multiply(x,v),y),additive_inverse(multiply(x,multiply(v,y)))))),
inference(superposition,[],[f21,f15]) ).
fof(f49,plain,
! [X0,X1] : additive_identity = add(X0,add(X1,additive_inverse(add(X0,X1)))),
inference(superposition,[],[f10,f15]) ).
fof(f51,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f52,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,u),y),add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(v,y))),additive_inverse(multiply(x,multiply(u,y)))))),
inference(forward_demodulation,[],[f47,f51]) ).
fof(f54,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f39,f1]) ).
fof(f55,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,u),y),add(multiply(multiply(x,v),y),add(additive_inverse(multiply(x,multiply(u,y))),additive_inverse(multiply(x,multiply(v,y)))))),
inference(forward_demodulation,[],[f52,f14]) ).
fof(f162,plain,
! [X0,X1] : add(X0,additive_identity) = add(X1,additive_inverse(add(additive_inverse(X0),X1))),
inference(superposition,[],[f54,f49]) ).
fof(f163,plain,
! [X0,X1] : add(X1,additive_inverse(add(additive_inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f162,f2]) ).
fof(f196,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(f225,plain,
! [X0,X1] : add(X1,X0) = additive_inverse(add(additive_inverse(X0),additive_inverse(X1))),
inference(superposition,[],[f54,f163]) ).
fof(f957,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
inference(superposition,[],[f11,f225]) ).
fof(f1451,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(multiply(x,u),y),add(multiply(multiply(x,v),y),additive_inverse(add(multiply(x,multiply(v,y)),multiply(x,multiply(u,y)))))),
inference(superposition,[],[f55,f957]) ).
fof(f1493,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(add(multiply(x,u),multiply(x,v)),y),additive_inverse(add(multiply(x,multiply(v,y)),multiply(x,multiply(u,y))))),
inference(forward_demodulation,[],[f1451,f196]) ).
fof(f1519,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(add(multiply(x,u),multiply(x,v)),y),additive_inverse(add(multiply(x,multiply(u,y)),multiply(x,multiply(v,y))))),
inference(forward_demodulation,[],[f1493,f14]) ).
fof(f1540,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(add(multiply(x,u),multiply(x,v)),y),additive_inverse(multiply(x,add(multiply(u,y),multiply(v,y))))),
inference(forward_demodulation,[],[f1519,f12]) ).
fof(f1550,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(multiply(add(multiply(x,u),multiply(x,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))),
inference(forward_demodulation,[],[f1540,f13]) ).
fof(f1555,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(add(multiply(x,u),multiply(x,v)),y)),
inference(forward_demodulation,[],[f1550,f14]) ).
fof(f1558,plain,
add(multiply(multiply(x,add(u,v)),y),additive_inverse(multiply(x,multiply(add(u,v),y)))) != add(additive_inverse(multiply(x,multiply(add(u,v),y))),multiply(multiply(x,add(u,v)),y)),
inference(forward_demodulation,[],[f1555,f12]) ).
fof(f1560,plain,
$false,
inference(forward_subsumption_resolution,[],[f1558,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG020-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 23:05:17 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.45 Running first-order model finding
% 0.14/0.45 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.56 % (4069383)Will run a generic schedule for satisfiability detection.
% 0.21/0.56 % (4069389)% WARNING: option uhcvi not known.
% 0.21/0.56 % (4069389)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2294294609:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.56 % (4069390)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2844748204:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.56 % (4069388)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=270326029_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.56 % (4069391)dis+10_1_sil=32000:sp=arity:random_seed=1084614190:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.56 % (4069392)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2540648000:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.56 % (4069393)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1874587331:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.56 % (4069394)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4239579027:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.56 % TRYING [1]
% 0.21/0.56 % TRYING [2]
% 0.21/0.56 % TRYING [3]
% 0.21/0.56 % TRYING [4]
% 0.21/0.56 % (4069392) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4069383-4069392"...
% 0.21/0.56 % (4069393) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4069383-4069393"...
% 0.21/0.56 % (4069392)...printing done.
% 0.21/0.56 % (4069392)Refutation found. Thanks to Tanya!
% 0.21/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56 % (4069392)------------------------------
% 0.21/0.56 % (4069392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.56 % (4069392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.56 % (4069392)CaDiCaL version: 2.1.3
% 0.21/0.56 % (4069392)Termination reason: Refutation
% 0.21/0.56 % (4069392)Time elapsed: 0.056 s
% 0.21/0.56 % (4069392)Peak memory usage: 12 MB
% 0.21/0.56 % (4069392)Instructions burned: 56 (million)
% 0.21/0.56 % (4069383)Success in time 0.097 s
% 0.21/0.56 % Vampire exiting
%------------------------------------------------------------------------------