%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 10:16:35 AM UTC 2026
% Result : Unsatisfiable 1.42s 0.71s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 41 unt; 3 def)
% Number of atoms : 80 ( 51 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 19 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 132 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : divide(inverse(divide(divide(divide(X0,X0),X1),divide(X2,divide(X1,X3)))),X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,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)) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2]) ).
fof(f7,definition,
( spl0_1
<=> divide(divide(a3,inverse(b3)),inverse(c3)) = divide(a3,inverse(divide(b3,inverse(c3)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f11,definition,
( spl0_2
<=> a2 = divide(divide(inverse(b2),inverse(b2)),inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_3
<=> divide(inverse(a1),inverse(a1)) = divide(inverse(b1),inverse(b1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f5,f15,f11,f7]) ).
fof(f19,plain,
! [X2,X3,X0,X1,X4,X5] : divide(inverse(divide(divide(divide(X1,X1),inverse(divide(divide(divide(X2,X2),X3),divide(X0,divide(X3,X4))))),divide(X5,X0))),X4) = X5,
inference(superposition,[],[f1,f1]) ).
fof(f20,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(divide(divide(divide(X3,X3),X4),divide(X0,divide(X4,divide(X2,X5))))) = divide(inverse(divide(divide(divide(X1,X1),X2),X0)),X5),
inference(superposition,[],[f1,f1]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : divide(divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3),divide(X1,X3)) = X2,
inference(superposition,[],[f1,f20]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(divide(divide(divide(X0,X0),X1),divide(divide(X2,X3),divide(X1,divide(inverse(divide(divide(divide(X4,X4),X5),divide(X3,divide(X5,X6)))),X6))))) = X2,
inference(superposition,[],[f19,f20]) ).
fof(f57,plain,
! [X2,X3,X0,X1] : inverse(divide(divide(divide(X0,X0),X1),divide(divide(X2,X3),divide(X1,X3)))) = X2,
inference(forward_demodulation,[],[f54,f1]) ).
fof(f60,plain,
! [X2,X3,X0,X1,X4] : divide(divide(inverse(divide(X0,X3)),X4),divide(divide(X2,inverse(divide(divide(divide(X1,X1),X2),X0))),X4)) = X3,
inference(superposition,[],[f46,f46]) ).
fof(f95,plain,
! [X2,X3,X0,X4] : divide(divide(X0,X3),divide(X2,X3)) = divide(divide(X0,X4),divide(X2,X4)),
inference(superposition,[],[f46,f57]) ).
fof(f141,plain,
! [X2,X3,X0,X1,X4] : divide(divide(inverse(divide(divide(divide(X0,X1),divide(X2,X1)),X3)),X4),divide(divide(X2,X0),X4)) = X3,
inference(superposition,[],[f46,f95]) ).
fof(f153,plain,
! [X2,X3,X0,X1,X4] : divide(X2,X3) = divide(divide(inverse(divide(divide(divide(X0,X0),X1),divide(X2,X1))),X4),divide(X3,X4)),
inference(superposition,[],[f46,f95]) ).
fof(f698,plain,
! [X2,X3,X0,X1,X4] : divide(X0,X4) = divide(X0,divide(X1,inverse(divide(divide(divide(X2,X2),X1),divide(divide(X3,X3),X4))))),
inference(superposition,[],[f60,f153]) ).
fof(f884,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : divide(X4,inverse(divide(divide(divide(X5,X5),X4),divide(divide(X6,X6),X3)))) = divide(divide(inverse(divide(divide(divide(X0,X1),divide(X2,X1)),X3)),X7),divide(divide(X2,X0),X7)),
inference(superposition,[],[f141,f698]) ).
fof(f893,plain,
! [X3,X6,X4,X5] : divide(X4,inverse(divide(divide(divide(X5,X5),X4),divide(divide(X6,X6),X3)))) = X3,
inference(forward_demodulation,[],[f884,f141]) ).
fof(f971,plain,
! [X2,X3,X0,X1] : divide(X3,inverse(divide(divide(divide(X0,X0),X1),divide(divide(X2,X2),X1)))) = X3,
inference(superposition,[],[f893,f95]) ).
fof(f1136,plain,
! [X2,X3,X0,X1,X4,X5] : divide(divide(X0,X5),divide(X4,X5)) = divide(X0,divide(X4,inverse(divide(divide(divide(X1,X1),X2),divide(divide(X3,X3),X2))))),
inference(superposition,[],[f95,f971]) ).
fof(f1201,plain,
! [X0,X4,X5] : divide(X0,X4) = divide(divide(X0,X5),divide(X4,X5)),
inference(forward_demodulation,[],[f1136,f971]) ).
fof(f1278,plain,
! [X2,X0,X1] : inverse(divide(divide(divide(X2,X2),X1),divide(X0,X1))) = X0,
inference(superposition,[],[f57,f1201]) ).
fof(f1400,plain,
! [X2,X0] : inverse(divide(divide(X2,X2),X0)) = X0,
inference(forward_demodulation,[],[f1278,f1201]) ).
fof(f1440,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(superposition,[],[f1400,f1201]) ).
fof(f1468,plain,
! [X3,X0,X1] : divide(divide(X0,X3),divide(divide(X1,X1),X3)) = X0,
inference(superposition,[],[f141,f1400]) ).
fof(f1471,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(forward_demodulation,[],[f1468,f1201]) ).
fof(f1525,plain,
! [X2,X0,X1] : divide(X2,X2) = divide(X1,inverse(divide(divide(X0,X0),X1))),
inference(superposition,[],[f893,f1471]) ).
fof(f1701,plain,
! [X2,X1] : divide(X1,X1) = divide(X2,X2),
inference(forward_demodulation,[],[f1525,f1400]) ).
fof(f2243,plain,
! [X0,X1] : divide(divide(X1,X1),X0) = inverse(X0),
inference(superposition,[],[f1440,f1471]) ).
fof(f2411,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f1400,f2243]) ).
fof(f2452,plain,
! [X2,X3,X0,X1,X4] : divide(inverse(divide(divide(divide(X4,X4),X2),X0)),X3) = inverse(inverse(divide(X0,divide(divide(X1,X1),divide(X2,X3))))),
inference(superposition,[],[f20,f2243]) ).
fof(f2514,plain,
! [X2,X3,X0,X1,X4] : divide(inverse(divide(divide(divide(X4,X4),X2),X0)),X3) = inverse(divide(divide(divide(X1,X1),divide(X2,X3)),X0)),
inference(forward_demodulation,[],[f2452,f1440]) ).
fof(f2642,plain,
! [X2,X3,X0,X1,X4] : divide(inverse(divide(divide(divide(X4,X4),X2),X0)),X3) = divide(X0,divide(divide(X1,X1),divide(X2,X3))),
inference(forward_demodulation,[],[f2514,f1440]) ).
fof(f2748,plain,
! [X2,X3,X0,X4] : divide(inverse(divide(divide(divide(X4,X4),X2),X0)),X3) = divide(X0,inverse(divide(X2,X3))),
inference(forward_demodulation,[],[f2642,f2243]) ).
fof(f2818,plain,
! [X2,X3,X0,X4] : divide(inverse(divide(divide(divide(X4,X4),X2),X0)),X3) = divide(X0,divide(X3,X2)),
inference(forward_demodulation,[],[f2748,f1440]) ).
fof(f2870,plain,
! [X2,X3,X0,X4] : divide(X0,divide(X3,X2)) = divide(divide(X0,divide(divide(X4,X4),X2)),X3),
inference(forward_demodulation,[],[f2818,f1440]) ).
fof(f2891,plain,
! [X2,X3,X0] : divide(X0,divide(X3,X2)) = divide(divide(X0,inverse(X2)),X3),
inference(forward_demodulation,[],[f2870,f2243]) ).
fof(f6831,plain,
( divide(a3,inverse(divide(b3,inverse(c3)))) != divide(a3,divide(inverse(c3),b3))
| spl0_1 ),
inference(superposition,[],[f9,f2891]) ).
fof(f6847,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(c3),b3))
| spl0_1 ),
inference(forward_demodulation,[],[f6831,f1440]) ).
fof(f6848,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f6847]) ).
fof(f6849,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f6848]) ).
fof(f7308,plain,
( a2 != inverse(inverse(a2))
| spl0_2 ),
inference(forward_demodulation,[],[f13,f2243]) ).
fof(f7309,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f7308,f2411]) ).
fof(f7310,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f7309]) ).
fof(f7312,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f17,f1701]) ).
fof(f7313,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f7312]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f18]) ).
cnf(s1781,plain,
spl0_1,
inference(sat_conversion,[],[f6849]) ).
cnf(s1863,plain,
spl0_2,
inference(sat_conversion,[],[f7310]) ).
cnf(s1864,plain,
spl0_3,
inference(sat_conversion,[],[f7313]) ).
cnf(s1865,plain,
$false,
inference(rat,[],[s4,s1864,s1863,s1781]) ).
fof(f7314,plain,
$false,
inference(avatar_sat_refutation,[],[s1865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n004.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 09:18:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 1.42/0.71 % (3242725)Will run a generic schedule for satisfiability detection.
% 1.42/0.71 % (3242731)% WARNING: option uhcvi not known.
% 1.42/0.71 % (3242736)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3782119701:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.42/0.71 % (3242732)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2065607886:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.42/0.71 % (3242731)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=220346283:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.42/0.71 % (3242733)dis+10_1_sil=32000:sp=arity:random_seed=3393593918:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.42/0.71 % (3242730)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3288428337_2999 on theBenchmark for (2999ds/0Mi)
% 1.42/0.71 % (3242734)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1586771832:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.42/0.71 % TRYING [1]
% 1.42/0.71 % TRYING [2]
% 1.42/0.71 % (3242735)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3263333206:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.42/0.71 % TRYING [3]
% 1.42/0.71 % TRYING [4]
% 1.42/0.71 % (3242736)Instruction limit reached!
% 1.42/0.71 % (3242736)------------------------------
% 1.42/0.71 % (3242736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.71 % (3242736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.71 % (3242736)CaDiCaL version: 2.1.3
% 1.42/0.71 % (3242736)Termination reason: Instruction limit
% 1.42/0.71 % (3242736)Termination phase: Saturation
% 1.42/0.71 % (3242736)Time elapsed: 0.082 s
% 1.42/0.71 % (3242736)Peak memory usage: 13 MB
% 1.42/0.71 % (3242736)Instructions burned: 161 (million)
% 1.42/0.71 % (3242735)Instruction limit reached!
% 1.42/0.71 % (3242735)------------------------------
% 1.42/0.71 % (3242735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.71 % (3242735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.71 % (3242735)CaDiCaL version: 2.1.3
% 1.42/0.71 % (3242735)Termination reason: Instruction limit
% 1.42/0.71 % (3242735)Termination phase: Saturation
% 1.42/0.71 % (3242735)Time elapsed: 0.080 s
% 1.42/0.71 % (3242735)Peak memory usage: 13 MB
% 1.42/0.71 % (3242735)Instructions burned: 132 (million)
% 1.42/0.71 % (3242733)Instruction limit reached!
% 1.42/0.71 % (3242733)------------------------------
% 1.42/0.71 % (3242733)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.71 % (3242733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.71 % (3242733)CaDiCaL version: 2.1.3
% 1.42/0.71 % (3242733)Termination reason: Instruction limit
% 1.42/0.71 % (3242733)Termination phase: Saturation
% 1.42/0.71 % (3242733)Time elapsed: 0.090 s
% 1.42/0.71 % (3242733)Peak memory usage: 12 MB
% 1.42/0.71 % (3242733)Instructions burned: 104 (million)
% 1.42/0.71 % (3242752)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1117905459:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.42/0.71 % TRYING [1]
% 1.42/0.71 % TRYING [2]
% 1.42/0.71 % TRYING [3]
% 1.42/0.71 % TRYING [4]
% 1.42/0.71 % (3242734)Instruction limit reached!
% 1.42/0.71 % (3242734)------------------------------
% 1.42/0.71 % (3242734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.71 % (3242734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.71 % (3242734)CaDiCaL version: 2.1.3
% 1.42/0.71 % (3242734)Termination reason: Instruction limit
% 1.42/0.71 % (3242734)Termination phase: Saturation
% 1.42/0.71 % (3242734)Time elapsed: 0.103 s
% 1.42/0.71 % (3242734)Peak memory usage: 12 MB
% 1.42/0.71 % (3242734)Instructions burned: 117 (million)
% 1.42/0.71 % (3242753)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1077770627:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.42/0.71 % (3242754)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=533465538:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.42/0.71 % (3242757)ott-21_1_sil=16000:fs=off:random_seed=3226168064:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.42/0.71 % TRYING [5]
% 1.42/0.71 % (3242753)Instruction limit reached!
% 1.42/0.71 % (3242753)------------------------------
% 1.42/0.71 % (3242753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.71 % (3242753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.71 % (3242753)CaDiCaL version: 2.1.3
% 1.42/0.71 % (3242753)Termination reason: Instruction limit
% 1.42/0.71 % (3242753)Termination phase: Saturation
% 1.42/0.71 % (3242753)Time elapsed: 0.106 s
% 1.42/0.71 % (3242753)Peak memory usage: 13 MB
% 1.42/0.71 % (3242753)Instructions burned: 132 (million)
% 1.42/0.71 % (3242762)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4001812171:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.42/0.71 % (3242732) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3242725-3242732"...
% 1.42/0.71 % (3242732)...printing done.
% 1.42/0.71 % (3242732)Refutation found. Thanks to Tanya!
% 1.42/0.71 % SZS status Unsatisfiable for theBenchmark
% 1.42/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.71 % (3242732)------------------------------
% 1.42/0.71 % (3242732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.71 % (3242732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.71 % (3242732)CaDiCaL version: 2.1.3
% 1.42/0.71 % (3242732)Termination reason: Refutation
% 1.42/0.71 % (3242732)Time elapsed: 0.242 s
% 1.42/0.71 % (3242732)Peak memory usage: 16 MB
% 1.42/0.71 % (3242732)Instructions burned: 296 (million)
% 1.42/0.71 % (3242725)Success in time 0.288 s
% 1.42/0.71 % Vampire exiting
%------------------------------------------------------------------------------