%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 09:36:12 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 7
% Syntax : Number of formulae : 76 ( 76 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_add_property) ).
fof(f3,axiom,
! [X0] : add(X0,inverse(X0)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse) ).
fof(f4,axiom,
! [X2,X0,X1] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),add(multiply(X0,X2),multiply(inverse(X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley_defn) ).
fof(f5,axiom,
! [X0,X1] : pixley(X0,X0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley1) ).
fof(f6,axiom,
! [X0,X1] : pixley(X0,X1,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pixley2) ).
fof(f8,negated_conjecture,
add(multiply(a,b),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_add_multiply) ).
fof(f9,plain,
b != add(multiply(a,b),b),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),add(multiply(X0,X1),multiply(inverse(X0),X1))) = X1,
inference(definition_unfolding,[],[f5,f4]) ).
fof(f11,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),add(multiply(X0,X1),multiply(inverse(X1),X1))) = X0,
inference(definition_unfolding,[],[f6,f4]) ).
fof(f13,plain,
! [X0] : inverse(X0) = multiply(n1,inverse(X0)),
inference(superposition,[],[f1,f3]) ).
fof(f14,plain,
! [X2,X0,X1] : multiply(X0,add(add(X1,X0),X2)) = add(X0,multiply(X2,X0)),
inference(superposition,[],[f2,f1]) ).
fof(f15,plain,
! [X0,X1] : multiply(inverse(X0),add(n1,X1)) = add(inverse(X0),multiply(X1,inverse(X0))),
inference(superposition,[],[f2,f13]) ).
fof(f16,plain,
! [X2,X0,X1] : multiply(X0,add(X1,add(X2,X0))) = add(multiply(X1,X0),X0),
inference(superposition,[],[f2,f1]) ).
fof(f17,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,n1)) = add(multiply(X1,inverse(X0)),inverse(X0)),
inference(superposition,[],[f2,f13]) ).
fof(f18,plain,
! [X2,X0,X1] : multiply(X2,X0) = multiply(multiply(X0,add(X1,X2)),multiply(X2,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f21,plain,
! [X0,X1] : add(X0,multiply(inverse(add(X1,X0)),X0)) = multiply(X0,n1),
inference(superposition,[],[f14,f3]) ).
fof(f24,plain,
! [X0] : multiply(inverse(X0),n1) = add(inverse(X0),multiply(inverse(n1),inverse(X0))),
inference(superposition,[],[f21,f3]) ).
fof(f39,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(multiply(X1,n1),multiply(inverse(X0),X1)),
inference(superposition,[],[f18,f3]) ).
fof(f73,plain,
! [X0] : add(inverse(X0),inverse(X0)) = multiply(inverse(X0),add(n1,n1)),
inference(superposition,[],[f15,f13]) ).
fof(f90,plain,
! [X0] : add(inverse(X0),inverse(X0)) = multiply(multiply(add(n1,n1),n1),add(inverse(X0),inverse(X0))),
inference(superposition,[],[f39,f73]) ).
fof(f96,plain,
! [X0] : add(inverse(X0),inverse(X0)) = multiply(n1,add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[],[f90,f1]) ).
fof(f117,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),multiply(X1,add(X0,inverse(X0)))) = X1,
inference(forward_demodulation,[],[f10,f2]) ).
fof(f118,plain,
! [X0,X1] : add(multiply(X0,inverse(X0)),multiply(X1,n1)) = X1,
inference(forward_demodulation,[],[f117,f3]) ).
fof(f119,plain,
! [X0] : add(inverse(n1),multiply(X0,n1)) = X0,
inference(superposition,[],[f118,f13]) ).
fof(f126,plain,
! [X0] : add(X0,n1) = add(inverse(n1),n1),
inference(superposition,[],[f119,f1]) ).
fof(f132,plain,
! [X0,X1] : add(X1,n1) = add(X0,n1),
inference(superposition,[],[f126,f126]) ).
fof(f161,plain,
! [X0,X1] : multiply(X1,add(X0,n1)) = add(X1,multiply(n1,X1)),
inference(superposition,[],[f14,f132]) ).
fof(f163,plain,
! [X0,X1] : add(inverse(X1),inverse(X1)) = multiply(inverse(X1),add(X0,n1)),
inference(superposition,[],[f73,f132]) ).
fof(f551,plain,
! [X0,X1] : add(multiply(X0,inverse(X1)),multiply(X1,add(X0,inverse(X1)))) = X0,
inference(forward_demodulation,[],[f11,f2]) ).
fof(f560,plain,
inverse(n1) = add(multiply(inverse(n1),inverse(n1)),add(inverse(n1),inverse(n1))),
inference(superposition,[],[f551,f96]) ).
fof(f787,plain,
multiply(inverse(n1),inverse(n1)) = add(multiply(multiply(inverse(n1),inverse(n1)),inverse(n1)),inverse(n1)),
inference(superposition,[],[f16,f560]) ).
fof(f793,plain,
multiply(inverse(n1),inverse(n1)) = multiply(inverse(n1),add(multiply(inverse(n1),inverse(n1)),n1)),
inference(forward_demodulation,[],[f787,f17]) ).
fof(f794,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),multiply(n1,inverse(n1))),
inference(forward_demodulation,[],[f793,f161]) ).
fof(f795,plain,
multiply(inverse(n1),inverse(n1)) = multiply(inverse(n1),add(n1,n1)),
inference(forward_demodulation,[],[f794,f15]) ).
fof(f796,plain,
add(inverse(n1),inverse(n1)) = multiply(inverse(n1),inverse(n1)),
inference(forward_demodulation,[],[f795,f73]) ).
fof(f804,plain,
inverse(n1) = multiply(multiply(inverse(n1),inverse(n1)),inverse(n1)),
inference(superposition,[],[f1,f796]) ).
fof(f812,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),multiply(n1,add(multiply(inverse(n1),inverse(n1)),inverse(n1)))),
inference(superposition,[],[f551,f804]) ).
fof(f821,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),multiply(n1,multiply(inverse(n1),add(inverse(n1),n1)))),
inference(forward_demodulation,[],[f812,f17]) ).
fof(f823,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),multiply(n1,add(inverse(n1),inverse(n1)))),
inference(forward_demodulation,[],[f821,f163]) ).
fof(f825,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),add(inverse(n1),inverse(n1))),
inference(forward_demodulation,[],[f823,f96]) ).
fof(f826,plain,
multiply(inverse(n1),inverse(n1)) = add(inverse(n1),multiply(inverse(n1),inverse(n1))),
inference(forward_demodulation,[],[f825,f796]) ).
fof(f827,plain,
multiply(inverse(n1),inverse(n1)) = multiply(inverse(n1),n1),
inference(forward_demodulation,[],[f826,f24]) ).
fof(f830,plain,
multiply(inverse(n1),n1) = add(inverse(n1),multiply(inverse(n1),n1)),
inference(superposition,[],[f24,f827]) ).
fof(f841,plain,
inverse(n1) = multiply(inverse(n1),n1),
inference(forward_demodulation,[],[f830,f119]) ).
fof(f860,plain,
! [X0] : add(inverse(n1),multiply(X0,n1)) = multiply(n1,add(inverse(n1),X0)),
inference(superposition,[],[f2,f841]) ).
fof(f861,plain,
! [X0] : multiply(n1,add(inverse(n1),X0)) = X0,
inference(forward_demodulation,[],[f860,f119]) ).
fof(f911,plain,
! [X0] : multiply(X0,n1) = multiply(n1,X0),
inference(superposition,[],[f861,f119]) ).
fof(f912,plain,
! [X0] : n1 = multiply(n1,add(X0,n1)),
inference(superposition,[],[f861,f126]) ).
fof(f918,plain,
multiply(n1,n1) = inverse(inverse(n1)),
inference(superposition,[],[f861,f3]) ).
fof(f960,plain,
! [X0] : add(inverse(n1),multiply(n1,X0)) = X0,
inference(superposition,[],[f119,f911]) ).
fof(f1035,plain,
add(multiply(n1,n1),multiply(n1,n1)) = multiply(n1,add(multiply(n1,n1),multiply(n1,n1))),
inference(superposition,[],[f96,f918]) ).
fof(f1041,plain,
multiply(n1,add(n1,n1)) = multiply(n1,multiply(n1,add(n1,n1))),
inference(forward_demodulation,[],[f1035,f2]) ).
fof(f1046,plain,
n1 = multiply(n1,n1),
inference(forward_demodulation,[],[f1041,f912]) ).
fof(f1052,plain,
! [X0] : add(n1,n1) = multiply(n1,add(X0,n1)),
inference(superposition,[],[f161,f1046]) ).
fof(f1064,plain,
n1 = add(n1,n1),
inference(forward_demodulation,[],[f1052,f912]) ).
fof(f1071,plain,
! [X0] : n1 = add(X0,n1),
inference(superposition,[],[f1064,f132]) ).
fof(f1252,plain,
! [X0] : inverse(X0) = add(inverse(n1),inverse(X0)),
inference(superposition,[],[f960,f13]) ).
fof(f1287,plain,
n1 = inverse(inverse(n1)),
inference(superposition,[],[f1252,f3]) ).
fof(f1324,plain,
! [X0] : add(multiply(X0,n1),multiply(inverse(n1),add(X0,n1))) = X0,
inference(superposition,[],[f551,f1287]) ).
fof(f1328,plain,
! [X0] : add(multiply(X0,n1),add(inverse(n1),inverse(n1))) = X0,
inference(forward_demodulation,[],[f1324,f163]) ).
fof(f1337,plain,
! [X0] : add(multiply(X0,n1),multiply(inverse(n1),inverse(n1))) = X0,
inference(forward_demodulation,[],[f1328,f796]) ).
fof(f1341,plain,
! [X0] : add(multiply(X0,n1),multiply(inverse(n1),n1)) = X0,
inference(forward_demodulation,[],[f1337,f827]) ).
fof(f1344,plain,
! [X0] : multiply(n1,add(X0,inverse(n1))) = X0,
inference(forward_demodulation,[],[f1341,f2]) ).
fof(f1425,plain,
! [X0] : multiply(inverse(n1),n1) = multiply(X0,multiply(inverse(n1),n1)),
inference(superposition,[],[f18,f1344]) ).
fof(f1432,plain,
! [X0] : multiply(n1,inverse(n1)) = multiply(X0,multiply(n1,inverse(n1))),
inference(forward_demodulation,[],[f1425,f911]) ).
fof(f1440,plain,
! [X0] : inverse(n1) = multiply(X0,inverse(n1)),
inference(forward_demodulation,[],[f1432,f13]) ).
fof(f1495,plain,
! [X0] : add(inverse(n1),multiply(n1,add(X0,inverse(n1)))) = X0,
inference(superposition,[],[f551,f1440]) ).
fof(f1516,plain,
! [X0] : add(X0,inverse(n1)) = X0,
inference(forward_demodulation,[],[f1495,f960]) ).
fof(f1523,plain,
! [X0] : multiply(n1,X0) = X0,
inference(superposition,[],[f1344,f1516]) ).
fof(f1549,plain,
! [X0] : multiply(X0,n1) = X0,
inference(superposition,[],[f1523,f911]) ).
fof(f1572,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = multiply(X0,add(X1,n1)),
inference(superposition,[],[f2,f1523]) ).
fof(f1597,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = multiply(X0,n1),
inference(forward_demodulation,[],[f1572,f1071]) ).
fof(f2395,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = X0,
inference(forward_demodulation,[],[f1597,f1549]) ).
fof(f2452,plain,
b != b,
inference(superposition,[],[f9,f2395]) ).
fof(f2496,plain,
$false,
inference(trivial_inequality_removal,[],[f2452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO024-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:07:22 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.19/0.32 % (764324)Will run a generic schedule for satisfiability detection.
% 0.19/0.32 % (764329)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3929859993_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.32 % TRYING [1]
% 0.19/0.32 % TRYING [2]
% 0.19/0.32 % TRYING [3]
% 0.19/0.32 % (764330)% WARNING: option uhcvi not known.
% 0.19/0.32 % TRYING [4]
% 0.19/0.32 % (764331)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2661762958:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.32 % (764330)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2468796799:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.32 % (764332)dis+10_1_sil=32000:sp=arity:random_seed=1473689699:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.32 % (764333)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3962422165:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.32 % (764335)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4043354400:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.32 % (764334)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=242209548:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % TRYING [5]
% 0.19/0.32 % (764331) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-764324-764331"...
% 0.19/0.32 % (764331)...printing done.
% 0.19/0.32 % (764331)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.32 % (764331)------------------------------
% 0.19/0.32 % (764331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (764331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (764331)CaDiCaL version: 2.1.3
% 0.19/0.32 % (764331)Termination reason: Refutation
% 0.19/0.32 % (764331)Time elapsed: 0.050 s
% 0.19/0.32 % (764331)Peak memory usage: 12 MB
% 0.19/0.32 % (764331)Instructions burned: 90 (million)
% 0.19/0.32 % (764324)Success in time 0.086 s
% 0.19/0.32 % Vampire exiting
%------------------------------------------------------------------------------