%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG008-4 : 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 : n020.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 12:35:42 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.61s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
fof(f3,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',distribute2) ).
fof(f8,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
fof(f14,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
fof(f15,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
fof(f16,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
fof(f18,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
fof(f20,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
fof(f21,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f22,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f23,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(forward_demodulation,[],[f3,f18]) ).
fof(f40,plain,
! [X0] : additive_inverse(X0) = multiply(X0,additive_inverse(X0)),
inference(superposition,[],[f14,f20]) ).
fof(f78,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = multiply(additive_inverse(X0),additive_inverse(X0)),
inference(superposition,[],[f16,f40]) ).
fof(f82,plain,
! [X0] : additive_inverse(X0) = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[],[f78,f20]) ).
fof(f86,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[],[f82,f8]) ).
fof(f143,plain,
! [X0] : additive_identity = add(X0,X0),
inference(superposition,[],[f24,f86]) ).
fof(f152,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[],[f17,f24]) ).
fof(f165,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(superposition,[],[f18,f17]) ).
fof(f171,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f152,f1]) ).
fof(f174,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(forward_demodulation,[],[f171,f86]) ).
fof(f248,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[],[f4,f20]) ).
fof(f310,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[],[f5,f20]) ).
fof(f315,plain,
! [X0] : multiply(add(a,X0),b) = add(c,multiply(X0,b)),
inference(superposition,[],[f5,f21]) ).
fof(f486,plain,
multiply(add(a,b),b) = add(c,b),
inference(superposition,[],[f315,f20]) ).
fof(f503,plain,
multiply(add(a,b),b) = add(b,c),
inference(forward_demodulation,[],[f486,f18]) ).
fof(f1185,plain,
multiply(add(a,b),add(add(a,b),b)) = add(add(a,b),add(b,c)),
inference(superposition,[],[f248,f503]) ).
fof(f1236,plain,
multiply(add(a,b),add(add(a,b),b)) = add(c,add(add(a,b),b)),
inference(forward_demodulation,[],[f1185,f165]) ).
fof(f1261,plain,
multiply(add(a,b),add(add(a,b),b)) = add(b,add(c,add(a,b))),
inference(forward_demodulation,[],[f1236,f165]) ).
fof(f1278,plain,
multiply(add(a,b),add(add(a,b),b)) = add(b,add(b,add(c,a))),
inference(forward_demodulation,[],[f1261,f165]) ).
fof(f1286,plain,
add(c,a) = multiply(add(a,b),add(add(a,b),b)),
inference(forward_demodulation,[],[f1278,f174]) ).
fof(f1290,plain,
add(c,a) = multiply(add(a,b),add(b,add(a,b))),
inference(forward_demodulation,[],[f1286,f18]) ).
fof(f1291,plain,
add(c,a) = multiply(add(a,b),add(a,add(b,b))),
inference(forward_demodulation,[],[f1290,f165]) ).
fof(f1292,plain,
add(c,a) = multiply(add(a,b),add(a,additive_identity)),
inference(forward_demodulation,[],[f1291,f143]) ).
fof(f1293,plain,
add(c,a) = multiply(add(a,b),add(additive_identity,a)),
inference(forward_demodulation,[],[f1292,f18]) ).
fof(f1294,plain,
add(c,a) = multiply(add(a,b),a),
inference(forward_demodulation,[],[f1293,f1]) ).
fof(f1295,plain,
add(a,c) = multiply(add(a,b),a),
inference(forward_demodulation,[],[f1294,f18]) ).
fof(f2198,plain,
add(a,add(a,c)) = multiply(add(a,add(a,b)),a),
inference(superposition,[],[f310,f1295]) ).
fof(f2201,plain,
multiply(b,a) = add(a,add(a,c)),
inference(forward_demodulation,[],[f2198,f174]) ).
fof(f2213,plain,
c = multiply(b,a),
inference(forward_demodulation,[],[f2201,f174]) ).
fof(f2223,plain,
$false,
inference(forward_subsumption_resolution,[],[f2213,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.46 % Computer : n020.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 27 22:59:19 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.52 Running first-order model finding
% 0.22/0.52 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
% 0.22/0.61 % (3866742)Will run a generic schedule for satisfiability detection.
% 0.22/0.61 % (3866751)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=873184277:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.61 % (3866748)% WARNING: option uhcvi not known.
% 0.22/0.61 % (3866749)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=184329889:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.61 % (3866750)dis+10_1_sil=32000:sp=arity:random_seed=2559760514:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.61 % (3866747)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1885908032_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.61 % (3866752)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3816036097:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.61 % (3866748)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1342386435:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.61 % (3866753)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3304359930:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.61 % TRYING [1]
% 0.22/0.61 % TRYING [2]
% 0.22/0.61 % TRYING [3]
% 0.22/0.61 % TRYING [4]
% 0.22/0.61 % (3866751) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3866742-3866751"...
% 0.22/0.61 % (3866751)...printing done.
% 0.22/0.61 % (3866751)Refutation found. Thanks to Tanya!
% 0.22/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.61 % (3866751)------------------------------
% 0.22/0.61 % (3866751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.61 % (3866751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.61 % (3866751)CaDiCaL version: 2.1.3
% 0.22/0.61 % (3866751)Termination reason: Refutation
% 0.22/0.61 % (3866751)Time elapsed: 0.033 s
% 0.22/0.61 % (3866751)Peak memory usage: 12 MB
% 0.22/0.61 % (3866751)Instructions burned: 64 (million)
% 0.22/0.61 % (3866742)Success in time 0.076 s
% 0.22/0.61 % Vampire exiting
%------------------------------------------------------------------------------