%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG019-7 : 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 : 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 12:35:44 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 20 ( 20 ~; 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 : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(f28,axiom,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X1)),additive_inverse(multiply(X0,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference3) ).
fof(f30,negated_conjecture,
associator(x,y,add(u,v)) != add(associator(x,y,u),associator(x,y,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_linearised_form1) ).
fof(f31,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,[],[f30,f18,f18,f18]) ).
fof(f32,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[],[f23,f25]) ).
fof(f99,plain,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X1,add(X0,X2)),
inference(superposition,[],[f15,f14]) ).
fof(f109,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f14,f15]) ).
fof(f217,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X2,X1)) = add(multiply(additive_inverse(X0),X2),multiply(X0,additive_inverse(X1))),
inference(superposition,[],[f12,f32]) ).
fof(f220,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),add(multiply(X0,X2),X3)) = add(multiply(X0,add(X1,X2)),X3),
inference(superposition,[],[f15,f12]) ).
fof(f223,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X2,X1)) = add(multiply(X0,additive_inverse(X2)),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f217,f32]) ).
fof(f233,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X2,X1)) = multiply(X0,add(additive_inverse(X2),additive_inverse(X1))),
inference(forward_demodulation,[],[f223,f12]) ).
fof(f242,plain,
! [X2,X0,X1] : multiply(X0,add(additive_inverse(X2),additive_inverse(X1))) = multiply(X0,additive_inverse(add(X2,X1))),
inference(forward_demodulation,[],[f233,f32]) ).
fof(f642,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X2)),additive_inverse(multiply(X0,X1))),
inference(superposition,[],[f14,f28]) ).
fof(f643,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(additive_inverse(multiply(X0,X2)),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f642,f25]) ).
fof(f668,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = add(multiply(X0,additive_inverse(X2)),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f643,f25]) ).
fof(f693,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = multiply(X0,add(additive_inverse(X2),additive_inverse(X1))),
inference(forward_demodulation,[],[f668,f12]) ).
fof(f717,plain,
! [X2,X0,X1] : multiply(additive_inverse(X0),add(X1,X2)) = multiply(X0,additive_inverse(add(X2,X1))),
inference(forward_demodulation,[],[f693,f242]) ).
fof(f738,plain,
! [X2,X0,X1] : multiply(X0,additive_inverse(add(X2,X1))) = multiply(X0,additive_inverse(add(X1,X2))),
inference(forward_demodulation,[],[f717,f32]) ).
fof(f1111,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))))),
inference(superposition,[],[f31,f99]) ).
fof(f1147,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),u),add(add(multiply(multiply(x,y),v),additive_inverse(multiply(x,multiply(y,v)))),additive_inverse(multiply(x,multiply(y,u))))),
inference(forward_demodulation,[],[f1111,f109]) ).
fof(f1177,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),u),add(multiply(multiply(x,y),v),add(additive_inverse(multiply(x,multiply(y,v))),additive_inverse(multiply(x,multiply(y,u)))))),
inference(forward_demodulation,[],[f1147,f15]) ).
fof(f1190,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),add(additive_inverse(multiply(x,multiply(y,v))),additive_inverse(multiply(x,multiply(y,u))))),
inference(forward_demodulation,[],[f1177,f220]) ).
fof(f1196,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,v))))),
inference(forward_demodulation,[],[f1190,f109]) ).
fof(f1200,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(additive_inverse(multiply(x,multiply(y,u))),add(additive_inverse(multiply(x,multiply(y,v))),multiply(multiply(x,y),add(u,v)))),
inference(forward_demodulation,[],[f1196,f14]) ).
fof(f1202,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(additive_inverse(multiply(x,multiply(y,u))),add(multiply(x,additive_inverse(multiply(y,v))),multiply(multiply(x,y),add(u,v)))),
inference(forward_demodulation,[],[f1200,f25]) ).
fof(f1203,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(x,additive_inverse(multiply(y,v))),add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,u))))),
inference(forward_demodulation,[],[f1202,f109]) ).
fof(f1204,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(x,additive_inverse(multiply(y,v))),add(additive_inverse(multiply(x,multiply(y,u))),multiply(multiply(x,y),add(u,v)))),
inference(forward_demodulation,[],[f1203,f14]) ).
fof(f1205,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(x,additive_inverse(multiply(y,v))),add(multiply(x,additive_inverse(multiply(y,u))),multiply(multiply(x,y),add(u,v)))),
inference(forward_demodulation,[],[f1204,f25]) ).
fof(f1206,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(x,add(additive_inverse(multiply(y,v)),additive_inverse(multiply(y,u)))),multiply(multiply(x,y),add(u,v))),
inference(forward_demodulation,[],[f1205,f220]) ).
fof(f1207,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,add(additive_inverse(multiply(y,v)),additive_inverse(multiply(y,u))))),
inference(forward_demodulation,[],[f1206,f14]) ).
fof(f1208,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,additive_inverse(add(multiply(y,v),multiply(y,u))))),
inference(forward_demodulation,[],[f1207,f242]) ).
fof(f1209,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,additive_inverse(add(multiply(y,u),multiply(y,v))))),
inference(forward_demodulation,[],[f1208,f738]) ).
fof(f1210,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,additive_inverse(multiply(y,add(u,v))))),
inference(forward_demodulation,[],[f1209,f12]) ).
fof(f1211,plain,
add(multiply(multiply(x,y),add(u,v)),additive_inverse(multiply(x,multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
inference(forward_demodulation,[],[f1210,f25]) ).
fof(f1212,plain,
add(multiply(multiply(x,y),add(u,v)),multiply(x,additive_inverse(multiply(y,add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
inference(forward_demodulation,[],[f1211,f25]) ).
fof(f1213,plain,
add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))) != add(multiply(multiply(x,y),add(u,v)),multiply(x,multiply(y,additive_inverse(add(u,v))))),
inference(forward_demodulation,[],[f1212,f25]) ).
fof(f1214,plain,
$false,
inference(trivial_inequality_removal,[],[f1213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG019-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:58:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.48 % (3503811)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3503816)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1755327261_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % (3503817)% WARNING: option uhcvi not known.
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % (3503817)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2234394721:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3503818)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3261764809:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3503821)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3199719818:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3503819)dis+10_1_sil=32000:sp=arity:random_seed=1764741577:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3503820)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1078080153:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3503822)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2858002073:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (3503820) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3503811-3503820"...
% 0.17/0.48 % (3503820)...printing done.
% 0.17/0.48 % (3503820)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3503820)------------------------------
% 0.17/0.48 % (3503820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3503820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3503820)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3503820)Termination reason: Refutation
% 0.17/0.48 % (3503820)Time elapsed: 0.023 s
% 0.17/0.48 % (3503820)Peak memory usage: 12 MB
% 0.17/0.48 % (3503820)Instructions burned: 39 (million)
% 0.17/0.48 % (3503811)Success in time 0.057 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------