%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI691_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 09:33:40 AM UTC 2026
% Result : Theorem 2.63s 0.95s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 30 ( 24 unt; 0 typ; 10 def)
% Number of atoms : 36 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 0 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 27 ( 0 atm; 25 fun; 0 num; 2 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 2 ( 2 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
b: $int ).
tff(func_def_2,type,
f: $int > $int ).
tff(func_def_8,type,
sF0: $int ).
tff(func_def_9,type,
sF1: $int ).
tff(func_def_10,type,
sF2: $int ).
tff(func_def_11,type,
sF3: $int ).
tff(f1,axiom,
$product(a,b) = f($product(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq) ).
tff(f2,conjecture,
f(f($product(a,b))) = $product(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f3,negated_conjecture,
( ( ~ f(f($product(a,b))) ) = $product(b,a) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f15,plain,
! [X0: $int,X1: $int] : ( $product(X1,X0) = $product(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f22,plain,
f(f($product(a,b))) != $product(b,a),
inference(flattening,[],[f3]) ).
tff(f23,plain,
$product(a,b) = f($product(a,b)),
inference(cnf_transformation,[],[f1]) ).
tff(f24,plain,
f(f($product(a,b))) != $product(b,a),
inference(cnf_transformation,[],[f22]) ).
tff(f26,definition,
sF0 = $product(a,b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f27,plain,
$product(a,b) = sF0,
inference(reorient_equations,[],[f26]) ).
tff(f28,definition,
sF1 = f(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f29,plain,
f(sF0) = sF1,
inference(reorient_equations,[],[f28]) ).
tff(f30,definition,
sF2 = f(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f31,definition,
sF3 = $product(b,a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f32,plain,
$product(b,a) = sF3,
inference(reorient_equations,[],[f31]) ).
tff(f33,plain,
sF2 != sF3,
inference(definition_folding,[],[f24,f32,f30,f29,f27]) ).
tff(f34,plain,
$product(b,a) = sF0,
inference(forward_demodulation,[],[f27,f15]) ).
tff(f36,definition,
( spl4_1
<=> ( sF2 = f(sF1) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f39,plain,
spl4_1,
inference(avatar_split_clause,[],[f30,f36]) ).
tff(f41,definition,
( spl4_2
<=> ( $product(b,a) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f44,plain,
spl4_2,
inference(avatar_split_clause,[],[f32,f41]) ).
tff(f45,plain,
$product(b,a) = f($product(b,a)),
inference(forward_demodulation,[],[f23,f15]) ).
tff(f47,definition,
( spl4_3
<=> ( sF2 = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f50,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f33,f47]) ).
tff(f52,definition,
( spl4_4
<=> ( f(sF0) = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f55,plain,
spl4_4,
inference(avatar_split_clause,[],[f29,f52]) ).
tff(f57,definition,
( spl4_5
<=> ( $product(b,a) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f60,plain,
spl4_5,
inference(avatar_split_clause,[],[f34,f57]) ).
tff(f62,definition,
( spl4_6
<=> ( $product(b,a) = f($product(b,a)) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
tff(f65,plain,
spl4_6,
inference(avatar_split_clause,[],[f45,f62]) ).
tff(f66,plain,
$false,
inference(avatar_smt_refutation,[],[f65,f60,f55,f50,f44,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI691_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:57:31 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.63/0.95 % (1165138)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.63/0.95 % (1165154)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1765345107:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.63/0.95 % (1165154)First to succeed.
% 2.63/0.95 % (1165154)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1165138"
% 2.63/0.95 % (1165147)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=522977415:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.63/0.95 % (1165152)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2498282255:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.63/0.95 % (1165151)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3162474580:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.63/0.95 % (1165149)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3057222037:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.63/0.95 % (1165148)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3546995341:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.63/0.95 % (1165145)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2180221007:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.63/0.95 % (1165149)Also succeeded, but the first one will report.
% 2.63/0.95 % (1165151)Instruction limit reached!
% 2.63/0.95 % (1165151)------------------------------
% 2.63/0.95 % (1165151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/0.95 % (1165151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.95 % (1165151)CaDiCaL version: 2.1.3
% 2.63/0.95 % (1165151)Termination reason: Instruction limit
% 2.63/0.95 % (1165151)Termination phase: Saturation
% 2.63/0.95 % (1165151)Time elapsed: 0.004 s
% 2.63/0.95 % (1165151)Peak memory usage: 89 MB
% 2.63/0.95 % (1165151)Instructions burned: 5 (million)
% 2.63/0.95 % (1165152)Also succeeded, but the first one will report.
% 2.63/0.95 % (1165145)Also succeeded, but the first one will report.
% 2.63/0.95 % (1165147)Also succeeded, but the first one will report.
% 2.63/0.95 % (1165148)Also succeeded, but the first one will report.
% 2.63/0.95 % (1165154)Refutation found. Thanks to Tanya!
% 2.63/0.95 % SZS status Theorem for theBenchmark
% 2.63/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/0.95 % (1165154)------------------------------
% 2.63/0.95 % (1165154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/0.95 % (1165154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/0.95 % (1165154)CaDiCaL version: 2.1.3
% 2.63/0.95 % (1165154)Termination reason: Refutation
% 2.63/0.95 % (1165154)Time elapsed: 0.021 s
% 2.63/0.95 % (1165154)Peak memory usage: 117 MB
% 2.63/0.95 % (1165154)Instructions burned: 11 (million)
% 2.63/0.95 % (1165154)------------------------------
% 2.63/0.95 % (1165154)------------------------------
% 2.63/0.95 % (1165138)Success in time 0.312 s
% 2.63/0.95 % Vampire exiting
%------------------------------------------------------------------------------