%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 10:13:09 AM UTC 2026
% Result : Unsatisfiable 11.34s 2.59s
% Output : Refutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of formulae : 131 ( 57 unt; 12 def)
% Number of atoms : 256 ( 103 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 246 ( 121 ~; 116 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_2) ).
fof(f21,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p19) ).
fof(f22,definition,
sF0 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
least_upper_bound(a,identity) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF1 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f25,plain,
greatest_lower_bound(a,identity) = sF1,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF2 = multiply(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f27,plain,
multiply(sF0,sF1) = sF2,
inference(reorient_equations,[],[f26]) ).
fof(f28,plain,
a != sF2,
inference(definition_folding,[],[f21,f27,f25,f23]) ).
fof(f32,definition,
( spl3_1
<=> least_upper_bound(a,identity) = sF0 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f34,plain,
( least_upper_bound(a,identity) = sF0
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
spl3_1,
inference(avatar_split_clause,[],[f23,f32]) ).
fof(f37,definition,
( spl3_2
<=> greatest_lower_bound(a,identity) = sF1 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f39,plain,
( greatest_lower_bound(a,identity) = sF1
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
spl3_2,
inference(avatar_split_clause,[],[f25,f37]) ).
fof(f41,plain,
( a = greatest_lower_bound(a,sF0)
| ~ spl3_1 ),
inference(superposition,[],[f12,f34]) ).
fof(f42,plain,
( a = greatest_lower_bound(sF0,a)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f41,f5]) ).
fof(f43,plain,
( a = least_upper_bound(a,sF1)
| ~ spl3_2 ),
inference(superposition,[],[f11,f39]) ).
fof(f44,plain,
( a = least_upper_bound(sF1,a)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f43,f6]) ).
fof(f46,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f50,definition,
( spl3_3
<=> multiply(sF0,sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f52,plain,
( multiply(sF0,sF1) = sF2
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
spl3_3,
inference(avatar_split_clause,[],[f27,f50]) ).
fof(f55,definition,
( spl3_4
<=> a = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f57,plain,
( a != sF2
| spl3_4 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
~ spl3_4,
inference(avatar_split_clause,[],[f28,f55]) ).
fof(f70,plain,
( identity = greatest_lower_bound(identity,sF0)
| ~ spl3_1 ),
inference(superposition,[],[f46,f34]) ).
fof(f74,plain,
( identity = greatest_lower_bound(sF0,identity)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f70,f5]) ).
fof(f115,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f125,plain,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X1,X2),multiply(X0,X2)),
inference(superposition,[],[f6,f15]) ).
fof(f128,plain,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = multiply(least_upper_bound(X1,X0),X2),
inference(forward_demodulation,[],[f125,f15]) ).
fof(f167,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(multiply(X1,X0),X0),
inference(superposition,[],[f16,f1]) ).
fof(f187,plain,
! [X0,X1] : multiply(greatest_lower_bound(X1,identity),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f167,f5]) ).
fof(f243,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f246,plain,
( ! [X0] : multiply(sF0,multiply(sF1,X0)) = multiply(sF2,X0)
| ~ spl3_3 ),
inference(superposition,[],[f4,f52]) ).
fof(f251,plain,
! [X2,X3,X0,X1] : multiply(least_upper_bound(X3,multiply(X0,X1)),X2) = least_upper_bound(multiply(X3,X2),multiply(X0,multiply(X1,X2))),
inference(superposition,[],[f15,f4]) ).
fof(f261,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f243,f1]) ).
fof(f274,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f261,f3]) ).
fof(f295,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f274,f19]) ).
fof(f313,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3),
inference(superposition,[],[f7,f14]) ).
fof(f324,plain,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(superposition,[],[f5,f7]) ).
fof(f350,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3),
inference(superposition,[],[f8,f13]) ).
fof(f363,plain,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X2,least_upper_bound(X0,X1)),
inference(superposition,[],[f6,f8]) ).
fof(f387,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(superposition,[],[f13,f295]) ).
fof(f819,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,greatest_lower_bound(X3,X2)),multiply(X1,X2)) = greatest_lower_bound(multiply(X0,X3),multiply(greatest_lower_bound(X0,X1),X2)),
inference(superposition,[],[f313,f16]) ).
fof(f909,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(X0,a),multiply(greatest_lower_bound(X0,X1),identity)) = greatest_lower_bound(multiply(X0,sF1),multiply(X1,identity))
| ~ spl3_2 ),
inference(superposition,[],[f819,f39]) ).
fof(f1038,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(X0,a),multiply(greatest_lower_bound(X0,X1),identity)) = greatest_lower_bound(multiply(X0,sF1),X1)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f909,f295]) ).
fof(f1074,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(X0,sF1),X1) = greatest_lower_bound(multiply(X0,a),greatest_lower_bound(X0,X1))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1038,f295]) ).
fof(f1089,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(X0,sF1),X1) = greatest_lower_bound(X0,greatest_lower_bound(X1,multiply(X0,a)))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f1074,f324]) ).
fof(f1130,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,least_upper_bound(X3,X2)),multiply(X1,X2)) = least_upper_bound(multiply(X0,X3),multiply(least_upper_bound(X0,X1),X2)),
inference(superposition,[],[f350,f15]) ).
fof(f1220,plain,
( ! [X0,X1] : least_upper_bound(multiply(X0,a),multiply(least_upper_bound(X0,X1),identity)) = least_upper_bound(multiply(X0,sF0),multiply(X1,identity))
| ~ spl3_1 ),
inference(superposition,[],[f1130,f34]) ).
fof(f1349,plain,
( ! [X0,X1] : least_upper_bound(multiply(X0,a),multiply(least_upper_bound(X0,X1),identity)) = least_upper_bound(multiply(X0,sF0),X1)
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1220,f295]) ).
fof(f1385,plain,
( ! [X0,X1] : least_upper_bound(multiply(X0,sF0),X1) = least_upper_bound(multiply(X0,a),least_upper_bound(X0,X1))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1349,f295]) ).
fof(f1400,plain,
( ! [X0,X1] : least_upper_bound(multiply(X0,sF0),X1) = least_upper_bound(X0,least_upper_bound(X1,multiply(X0,a)))
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1385,f363]) ).
fof(f1833,definition,
( spl3_6
<=> a = greatest_lower_bound(sF0,a) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f1835,plain,
( a = greatest_lower_bound(sF0,a)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f1833]) ).
fof(f1836,plain,
( spl3_6
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f42,f32,f1833]) ).
fof(f1950,definition,
( spl3_7
<=> a = least_upper_bound(sF1,a) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f1952,plain,
( a = least_upper_bound(sF1,a)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f1950]) ).
fof(f1953,plain,
( spl3_7
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f44,f37,f1950]) ).
fof(f2609,definition,
( spl3_8
<=> identity = greatest_lower_bound(sF0,identity) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f2611,plain,
( identity = greatest_lower_bound(sF0,identity)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f2609]) ).
fof(f2612,plain,
( spl3_8
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f74,f32,f2609]) ).
fof(f3272,plain,
( ! [X0] : multiply(sF1,X0) = greatest_lower_bound(X0,multiply(a,X0))
| ~ spl3_2 ),
inference(superposition,[],[f187,f39]) ).
fof(f3273,plain,
( ! [X0] : multiply(identity,X0) = greatest_lower_bound(X0,multiply(sF0,X0))
| ~ spl3_8 ),
inference(superposition,[],[f187,f2611]) ).
fof(f3398,plain,
( ! [X0] : greatest_lower_bound(X0,multiply(sF0,X0)) = X0
| ~ spl3_8 ),
inference(forward_demodulation,[],[f3273,f1]) ).
fof(f3458,plain,
( ! [X0] : least_upper_bound(X0,multiply(sF1,X0)) = X0
| ~ spl3_2 ),
inference(superposition,[],[f11,f3272]) ).
fof(f3469,plain,
( ! [X0] : multiply(a,greatest_lower_bound(X0,multiply(a,X0))) = multiply(sF1,multiply(a,X0))
| ~ spl3_2 ),
inference(superposition,[],[f14,f3272]) ).
fof(f3481,plain,
( ! [X0] : multiply(sF1,multiply(a,X0)) = multiply(a,multiply(sF1,X0))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f3469,f3272]) ).
fof(f7065,plain,
! [X2,X0,X1] : multiply(X0,multiply(least_upper_bound(identity,X1),X2)) = multiply(least_upper_bound(X0,multiply(X0,X1)),X2),
inference(superposition,[],[f4,f387]) ).
fof(f8473,plain,
( least_upper_bound(sF1,a) = least_upper_bound(multiply(sF1,sF0),a)
| ~ spl3_1
| ~ spl3_2 ),
inference(superposition,[],[f1400,f3458]) ).
fof(f8530,plain,
( least_upper_bound(sF1,a) = least_upper_bound(a,multiply(sF1,sF0))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f8473,f6]) ).
fof(f8558,plain,
( a = least_upper_bound(a,multiply(sF1,sF0))
| ~ spl3_1
| ~ spl3_2
| ~ spl3_7 ),
inference(forward_demodulation,[],[f8530,f1952]) ).
fof(f9840,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(multiply(sF0,sF1),a)
| ~ spl3_2
| ~ spl3_8 ),
inference(superposition,[],[f1089,f3398]) ).
fof(f9904,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(a,multiply(sF0,sF1))
| ~ spl3_2
| ~ spl3_8 ),
inference(forward_demodulation,[],[f9840,f5]) ).
fof(f9939,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(a,sF2)
| ~ spl3_2
| ~ spl3_3
| ~ spl3_8 ),
inference(forward_demodulation,[],[f9904,f52]) ).
fof(f9955,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(sF2,a)
| ~ spl3_2
| ~ spl3_3
| ~ spl3_8 ),
inference(forward_demodulation,[],[f9939,f5]) ).
fof(f9962,plain,
( a = greatest_lower_bound(sF2,a)
| ~ spl3_2
| ~ spl3_3
| ~ spl3_6
| ~ spl3_8 ),
inference(forward_demodulation,[],[f9955,f1835]) ).
fof(f9965,definition,
( spl3_21
<=> a = greatest_lower_bound(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl3_21])],[avatar_definition]) ).
fof(f9967,plain,
( a = greatest_lower_bound(sF2,a)
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f9965]) ).
fof(f9968,plain,
( spl3_21
| ~ spl3_2
| ~ spl3_3
| ~ spl3_6
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f9962,f2609,f1833,f50,f37,f9965]) ).
fof(f9970,plain,
( sF2 = least_upper_bound(sF2,a)
| ~ spl3_21 ),
inference(superposition,[],[f11,f9967]) ).
fof(f9996,definition,
( spl3_22
<=> sF2 = least_upper_bound(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl3_22])],[avatar_definition]) ).
fof(f9998,plain,
( sF2 = least_upper_bound(sF2,a)
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f9996]) ).
fof(f9999,plain,
( spl3_22
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f9970,f9965,f9996]) ).
fof(f10522,plain,
( ! [X0] : multiply(least_upper_bound(identity,a),multiply(sF1,X0)) = least_upper_bound(multiply(sF1,X0),multiply(sF1,multiply(a,X0)))
| ~ spl3_2 ),
inference(superposition,[],[f115,f3481]) ).
fof(f10549,plain,
( ! [X0] : multiply(least_upper_bound(identity,a),multiply(sF1,X0)) = multiply(least_upper_bound(sF1,multiply(sF1,a)),X0)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f10522,f251]) ).
fof(f10563,plain,
( ! [X0] : multiply(least_upper_bound(identity,a),multiply(sF1,X0)) = multiply(sF1,multiply(least_upper_bound(identity,a),X0))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f10549,f7065]) ).
fof(f10572,plain,
( ! [X0] : multiply(least_upper_bound(identity,a),multiply(sF1,X0)) = multiply(sF1,multiply(least_upper_bound(a,identity),X0))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f10563,f128]) ).
fof(f10579,plain,
( ! [X0] : multiply(least_upper_bound(identity,a),multiply(sF1,X0)) = multiply(sF1,multiply(sF0,X0))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f10572,f34]) ).
fof(f10581,plain,
( ! [X0] : multiply(sF1,multiply(sF0,X0)) = multiply(least_upper_bound(a,identity),multiply(sF1,X0))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f10579,f128]) ).
fof(f10582,plain,
( ! [X0] : multiply(sF0,multiply(sF1,X0)) = multiply(sF1,multiply(sF0,X0))
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f10581,f34]) ).
fof(f10583,plain,
( ! [X0] : multiply(sF2,X0) = multiply(sF1,multiply(sF0,X0))
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f10582,f246]) ).
fof(f10588,plain,
( multiply(sF2,identity) = multiply(sF1,sF0)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(superposition,[],[f10583,f295]) ).
fof(f10664,plain,
( sF2 = multiply(sF1,sF0)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f10588,f295]) ).
fof(f10681,plain,
( a = least_upper_bound(a,sF2)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_7 ),
inference(backward_demodulation,[],[f8558,f10664]) ).
fof(f10689,plain,
( a = least_upper_bound(sF2,a)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_7 ),
inference(forward_demodulation,[],[f10681,f6]) ).
fof(f10692,plain,
( a = sF2
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_7
| ~ spl3_22 ),
inference(forward_demodulation,[],[f10689,f9998]) ).
fof(f10693,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| ~ spl3_7
| ~ spl3_22 ),
inference(forward_subsumption_resolution,[],[f10692,f57]) ).
fof(f10694,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| ~ spl3_7
| ~ spl3_22 ),
inference(avatar_contradiction_clause,[],[f10693]) ).
cnf(s1,plain,
spl3_1,
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
spl3_3,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
~ spl3_4,
inference(sat_conversion,[],[f58]) ).
cnf(s6,plain,
( ~ spl3_1
| spl3_6 ),
inference(sat_conversion,[],[f1836]) ).
cnf(s7,plain,
( ~ spl3_2
| spl3_7 ),
inference(sat_conversion,[],[f1953]) ).
cnf(s8,plain,
( ~ spl3_1
| spl3_8 ),
inference(sat_conversion,[],[f2612]) ).
cnf(s21,plain,
( ~ spl3_2
| ~ spl3_3
| ~ spl3_6
| ~ spl3_8
| spl3_21 ),
inference(sat_conversion,[],[f9968]) ).
cnf(s22,plain,
( ~ spl3_21
| spl3_22 ),
inference(sat_conversion,[],[f9999]) ).
cnf(s25,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| spl3_4
| ~ spl3_7
| ~ spl3_22 ),
inference(sat_conversion,[],[f10694]) ).
cnf(s30,plain,
spl3_7,
inference(rat,[],[s7,s2]) ).
cnf(s34,plain,
~ spl3_22,
inference(rat,[],[s25,s30,s2,s4,s3,s1]) ).
cnf(s37,plain,
spl3_8,
inference(rat,[],[s8,s1]) ).
cnf(s38,plain,
spl3_6,
inference(rat,[],[s6,s1]) ).
cnf(s39,plain,
~ spl3_21,
inference(rat,[],[s22,s34]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s21,s39,s2,s3,s37,s38]) ).
fof(f10695,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:35:24 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.34/2.59 % (973991)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.34/2.59 % (974034)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2346768650:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.34/2.59 % (974033)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3192359693:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.34/2.59 % (974037)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1584470151:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.34/2.59 % (974035)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=808848241:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.34/2.59 % (974036)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4166075733:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.34/2.59 % (974031)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1979986554:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.34/2.59 % (974034)Instruction limit reached!
% 11.34/2.59 % (974034)------------------------------
% 11.34/2.59 % (974034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.34/2.59 % (974034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.34/2.59 % (974034)CaDiCaL version: 2.1.3
% 11.34/2.59 % (974034)Termination reason: Instruction limit
% 11.34/2.59 % (974034)Termination phase: Saturation
% 11.34/2.59 % (974034)Time elapsed: 0.044 s
% 11.34/2.59 % (974034)Peak memory usage: 89 MB
% 11.34/2.59 % (974034)Instructions burned: 138 (million)
% 11.34/2.59 % (974032)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3960251809:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.34/2.59 % (974035)Instruction limit reached!
% 11.34/2.59 % (974035)------------------------------
% 11.34/2.59 % (974035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.34/2.59 % (974035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.34/2.59 % (974035)CaDiCaL version: 2.1.3
% 11.34/2.59 % (974035)Termination reason: Instruction limit
% 11.34/2.59 % (974035)Termination phase: Saturation
% 11.34/2.59 % (974035)Time elapsed: 0.108 s
% 11.34/2.59 % (974035)Peak memory usage: 89 MB
% 11.34/2.59 % (974035)Instructions burned: 181 (million)
% 11.34/2.59 % (974036)Instruction limit reached!
% 11.34/2.59 % (974036)------------------------------
% 11.34/2.59 % (974036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.34/2.59 % (974036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.34/2.59 % (974036)CaDiCaL version: 2.1.3
% 11.34/2.59 % (974036)Termination reason: Instruction limit
% 11.34/2.59 % (974036)Termination phase: Saturation
% 11.34/2.59 % (974036)Time elapsed: 0.155 s
% 11.34/2.59 % (974036)Peak memory usage: 90 MB
% 11.34/2.59 % (974036)Instructions burned: 258 (million)
% 11.34/2.59 % (974044)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1741821692:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 11.34/2.59 % (974046)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2939983136:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 11.34/2.59 % (974047)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3821602148:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 11.34/2.59 % (974047)Instruction limit reached!
% 11.34/2.59 % (974047)------------------------------
% 11.34/2.59 % (974047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.34/2.59 % (974047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.34/2.59 % (974047)CaDiCaL version: 2.1.3
% 11.34/2.59 % (974047)Termination reason: Instruction limit
% 11.34/2.59 % (974047)Termination phase: Saturation
% 11.34/2.59 % (974047)Time elapsed: 0.153 s
% 11.34/2.59 % (974047)Peak memory usage: 91 MB
% 11.34/2.59 % (974047)Instructions burned: 215 (million)
% 11.34/2.59 % (974060)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=891830493:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 11.34/2.59 % (974037)Instruction limit reached!
% 11.34/2.59 % (974037)------------------------------
% 11.34/2.59 % (974037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.34/2.59 % (974037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.34/2.59 % (974037)CaDiCaL version: 2.1.3
% 11.34/2.59 % (974037)Termination reason: Instruction limit
% 11.34/2.59 % (974037)Termination phase: Saturation
% 11.34/2.59 % (974037)Time elapsed: 0.809 s
% 11.34/2.59 % (974037)Peak memory usage: 99 MB
% 11.34/2.59 % (974037)Instructions burned: 1188 (million)
% 11.34/2.59 % (974069)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=1336164128:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/12125Mi)
% 11.34/2.59 % (974060)Instruction limit reached!
% 11.34/2.59 % (974060)------------------------------
% 11.34/2.59 % (974060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.34/2.59 % (974060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.34/2.59 % (974060)CaDiCaL version: 2.1.3
% 11.34/2.59 % (974060)Termination reason: Instruction limit
% 11.34/2.59 % (974060)Termination phase: Saturation
% 11.34/2.59 % (974060)Time elapsed: 0.272 s
% 11.34/2.59 % (974060)Peak memory usage: 92 MB
% 11.34/2.59 % (974060)Instructions burned: 317 (million)
% 11.34/2.59 % (974072)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2189816867:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2987 on theBenchmark for (2987ds/2836Mi)
% 11.34/2.59 % (974031)First to succeed.
% 11.34/2.59 % (974031)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-973991"
% 11.34/2.59 % (974031)Refutation found. Thanks to Tanya!
% 11.34/2.59 % SZS status Unsatisfiable for theBenchmark
% 11.34/2.59 % SZS output start Proof for theBenchmark
% See solution above
% 12.55/2.79 % (974031)------------------------------
% 12.55/2.79 % (974031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.55/2.79 % (974031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.55/2.79 % (974031)CaDiCaL version: 2.1.3
% 12.55/2.79 % (974031)Termination reason: Refutation
% 12.55/2.79 % (974031)Time elapsed: 1.379 s
% 12.55/2.79 % (974031)Peak memory usage: 146 MB
% 12.55/2.79 % (974031)Instructions burned: 2660 (million)
% 12.55/2.79 % (974031)------------------------------
% 12.55/2.79 % (974031)------------------------------
% 12.55/2.79 % (973991)Success in time 1.708 s
% 12.55/2.79 % Vampire exiting
%------------------------------------------------------------------------------