%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 10:16:37 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.54s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 33 unt; 4 def)
% Number of atoms : 83 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 25 ~; 25 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f3,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
inference(reorient_equations,[],[f2]) ).
fof(f5,definition,
( spl0_1
<=> multiply(a4,b4) = multiply(b4,a4) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(a4,b4) != multiply(b4,a4)
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f9,definition,
( spl0_2
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f11,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f13,definition,
( spl0_3
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f15,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_3 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f17,definition,
( spl0_4
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f19,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| spl0_4 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f3,f17,f13,f9,f5]) ).
fof(f21,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,X3),inverse(multiply(multiply(multiply(X1,X0),X2),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f22,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f40,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,inverse(multiply(X1,X2))),inverse(X0)),
inference(superposition,[],[f21,f1]) ).
fof(f43,plain,
! [X2,X0,X1] : inverse(multiply(X1,multiply(X2,inverse(multiply(multiply(X1,X2),X0))))) = X0,
inference(superposition,[],[f21,f22]) ).
fof(f57,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,multiply(X1,X2))))) = X2,
inference(superposition,[],[f43,f21]) ).
fof(f74,plain,
! [X3,X0] : multiply(multiply(X3,X0),inverse(X3)) = X0,
inference(superposition,[],[f40,f43]) ).
fof(f99,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f74,f74]) ).
fof(f104,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = X0,
inference(superposition,[],[f1,f74]) ).
fof(f140,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f57,f99]) ).
fof(f181,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X1)),X0) = X0,
inference(superposition,[],[f104,f74]) ).
fof(f218,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f181,f140]) ).
fof(f237,plain,
! [X2,X0,X1] : multiply(multiply(multiply(multiply(X1,inverse(X1)),X2),X0),inverse(X0)) = X2,
inference(superposition,[],[f1,f181]) ).
fof(f241,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(multiply(multiply(X2,inverse(X2)),X1),inverse(X0)))) = X0,
inference(superposition,[],[f22,f181]) ).
fof(f253,plain,
! [X0,X1] : multiply(X1,inverse(inverse(multiply(X0,inverse(X0))))) = X1,
inference(superposition,[],[f104,f181]) ).
fof(f258,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(forward_demodulation,[],[f253,f140]) ).
fof(f261,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X1,inverse(X0)))) = X0,
inference(forward_demodulation,[],[f241,f181]) ).
fof(f265,plain,
! [X2,X0] : multiply(multiply(X2,X0),inverse(X0)) = X2,
inference(forward_demodulation,[],[f237,f181]) ).
fof(f330,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[],[f258,f181]) ).
fof(f375,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,inverse(inverse(X1))),
inference(superposition,[],[f265,f74]) ).
fof(f404,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f375,f140]) ).
fof(f460,plain,
( multiply(a4,b4) != multiply(a4,b4)
| spl0_1 ),
inference(superposition,[],[f7,f404]) ).
fof(f495,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f460]) ).
fof(f496,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f495]) ).
fof(f509,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_2 ),
inference(forward_demodulation,[],[f11,f404]) ).
fof(f886,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = multiply(X1,multiply(X2,X0)),
inference(superposition,[],[f261,f57]) ).
fof(f2518,plain,
! [X2,X0,X1] : multiply(X1,multiply(X2,X0)) = multiply(X0,multiply(X1,X2)),
inference(superposition,[],[f886,f404]) ).
fof(f3238,plain,
( multiply(a3,multiply(b3,c3)) != multiply(b3,multiply(c3,a3))
| spl0_2 ),
inference(superposition,[],[f509,f2518]) ).
fof(f3323,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f3238,f2518]) ).
fof(f3324,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f3323]) ).
fof(f3545,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f15,f218]) ).
fof(f3546,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f3545]) ).
fof(f3547,plain,
( multiply(inverse(a1),a1) != multiply(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f19,f404]) ).
fof(f3548,plain,
( multiply(b1,inverse(b1)) != multiply(a1,inverse(a1))
| spl0_4 ),
inference(forward_demodulation,[],[f3547,f404]) ).
fof(f3549,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f3548,f330]) ).
fof(f3550,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f3549]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f20]) ).
cnf(s310,plain,
spl0_1,
inference(sat_conversion,[],[f496]) ).
cnf(s1112,plain,
spl0_2,
inference(sat_conversion,[],[f3324]) ).
cnf(s1218,plain,
spl0_3,
inference(sat_conversion,[],[f3546]) ).
cnf(s1219,plain,
spl0_4,
inference(sat_conversion,[],[f3550]) ).
cnf(s1220,plain,
$false,
inference(rat,[],[s4,s1219,s1218,s1112,s310]) ).
fof(f3551,plain,
$false,
inference(avatar_sat_refutation,[],[s1220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:18:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.54 % (4149388)Will run a generic schedule for satisfiability detection.
% 0.16/0.54 % (4149396)dis+10_1_sil=32000:sp=arity:random_seed=3836273006:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.54 % (4149394)% WARNING: option uhcvi not known.
% 0.16/0.54 % (4149393)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2296968911_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.54 % (4149394)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=290772362:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.54 % (4149395)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3043364230:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.54 % (4149397)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1627967338:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.54 % (4149399)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2279404113:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.54 % (4149398)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2654355273:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.54 % TRYING [1]
% 0.16/0.54 % TRYING [2]
% 0.16/0.54 % TRYING [3]
% 0.16/0.54 % TRYING [4]
% 0.16/0.54 % (4149396)Instruction limit reached!
% 0.16/0.54 % (4149396)------------------------------
% 0.16/0.54 % (4149396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (4149396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (4149396)CaDiCaL version: 2.1.3
% 0.16/0.54 % (4149396)Termination reason: Instruction limit
% 0.16/0.54 % (4149396)Termination phase: Saturation
% 0.16/0.54 % (4149396)Time elapsed: 0.032 s
% 0.16/0.54 % (4149396)Peak memory usage: 12 MB
% 0.16/0.54 % (4149396)Instructions burned: 105 (million)
% 0.16/0.54 % (4149407)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2312292104:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.54 % TRYING [1]
% 0.16/0.54 % TRYING [2]
% 0.16/0.54 % TRYING [3]
% 0.16/0.54 % TRYING [4]
% 0.16/0.54 % (4149397)Instruction limit reached!
% 0.16/0.54 % (4149397)------------------------------
% 0.16/0.54 % (4149397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (4149397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (4149397)CaDiCaL version: 2.1.3
% 0.16/0.54 % (4149397)Termination reason: Instruction limit
% 0.16/0.54 % (4149397)Termination phase: Saturation
% 0.16/0.54 % (4149397)Time elapsed: 0.068 s
% 0.16/0.54 % (4149397)Peak memory usage: 13 MB
% 0.16/0.54 % (4149397)Instructions burned: 116 (million)
% 0.16/0.54 % (4149395) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4149388-4149395"...
% 0.16/0.54 % (4149395)...printing done.
% 0.16/0.54 % (4149395)Refutation found. Thanks to Tanya!
% 0.16/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.54 % (4149395)------------------------------
% 0.16/0.54 % (4149395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.54 % (4149395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.54 % (4149395)CaDiCaL version: 2.1.3
% 0.16/0.54 % (4149395)Termination reason: Refutation
% 0.16/0.54 % (4149395)Time elapsed: 0.073 s
% 0.16/0.54 % (4149395)Peak memory usage: 13 MB
% 0.16/0.54 % (4149395)Instructions burned: 130 (million)
% 0.16/0.54 % (4149388)Success in time 0.112 s
% 0.16/0.54 % Vampire exiting
%------------------------------------------------------------------------------