%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 : Fri Sep 25 01:29:57 PM UTC 2026
% Result : Unsatisfiable 3.60s 6.38s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 38
% Syntax : Number of formulae : 133 ( 88 unt; 3 def)
% Number of atoms : 222 ( 85 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 135 ( 58 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : group_member(identity_for(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',identity_in_group) ).
fof(f2,axiom,
! [X0,X1] : product(X0,identity_for(X0),X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',left_identity) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',right_identity) ).
fof(f5,axiom,
! [X0,X1] : product(X0,inverse(X0,X1),X1,identity_for(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',left_inverse) ).
fof(f6,axiom,
! [X0,X1] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',right_inverse) ).
fof(f7,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2,multiply(X1,X0,X2))
| ~ group_member(X2,X1)
| ~ group_member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function1_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( X4 = X3
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function2) ).
fof(f10,plain,
! [X2,X3,X0,X1,X4] :
( X3 = X4
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X1,X5,X6)
| ~ product(X0,X3,X4,X6)
| ~ product(X0,X2,X4,X5)
| ~ product(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',associativity1) ).
fof(f14,axiom,
group_member(b,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_group1) ).
fof(f15,axiom,
group_member(c,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_in_group1) ).
fof(f17,axiom,
group_member(g,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_in_group2) ).
fof(f18,axiom,
group_member(h,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_in_group2) ).
fof(f19,axiom,
! [X0] :
( X0 = c
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).
fof(f20,plain,
! [X0] :
( c = X0
| b = X0
| a = X0
| ~ group_member(X0,g1) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,axiom,
product(g1,a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
fof(f24,axiom,
product(g1,a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).
fof(f28,axiom,
product(g1,b,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_c) ).
fof(f29,axiom,
product(g1,b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_is_a) ).
fof(f30,axiom,
product(g1,c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_b_is_a) ).
fof(f31,axiom,
product(g1,c,c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_b) ).
fof(f32,axiom,
product(g2,f,f,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_f_is_f) ).
fof(f33,axiom,
product(g2,f,g,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_g_is_g) ).
fof(f34,axiom,
product(g2,g,f,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_f_is_g) ).
fof(f35,axiom,
product(g2,f,h,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_h_is_h) ).
fof(f36,axiom,
product(g2,h,f,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_f_is_h) ).
fof(f37,axiom,
product(g2,g,g,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_g_is_h) ).
fof(f38,axiom,
product(g2,g,h,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_h_is_f) ).
fof(f39,axiom,
product(g2,h,g,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_g_is_f) ).
fof(f40,axiom,
product(g2,h,h,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_h_is_g) ).
fof(f41,axiom,
an_isomorphism(a) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_f) ).
fof(f42,plain,
f = an_isomorphism(a),
inference(reorient_equations,[],[f41]) ).
fof(f43,axiom,
an_isomorphism(b) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_g) ).
fof(f44,plain,
g = an_isomorphism(b),
inference(reorient_equations,[],[f43]) ).
fof(f45,axiom,
an_isomorphism(c) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_maps_to_h) ).
fof(f46,plain,
h = an_isomorphism(c),
inference(reorient_equations,[],[f45]) ).
fof(f47,axiom,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_in_group1) ).
fof(f48,axiom,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_in_group1) ).
fof(f50,axiom,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
fof(f51,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
tcf(c_94,plain,
! [X0: $i] : group_member(identity_for(X0),X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : product(X0,identity_for(X0),X1,X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : product(X0,X1,identity_for(X0),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] : product(X0,inverse(X0,X1),X1,identity_for(X0)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2,multiply(X1,X0,X2))
| ~ group_member(X2,X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3 = X4 )
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X1,X5,X6)
| ~ product(X0,X3,X4,X6)
| ~ product(X0,X2,X4,X5)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_106,plain,
group_member(b,g1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_107,plain,
group_member(c,g1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_109,plain,
group_member(g,g2),
inference(cnf_transformation,[],[f17]) ).
tcf(c_110,plain,
group_member(h,g2),
inference(cnf_transformation,[],[f18]) ).
tcf(c_111,plain,
! [X0: $i] :
( ( X0 = c )
| ( X0 = b )
| ( X0 = a )
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_113,plain,
product(g1,a,a,a),
inference(cnf_transformation,[],[f23]) ).
tcf(c_114,plain,
product(g1,a,b,b),
inference(cnf_transformation,[],[f24]) ).
tcf(c_118,plain,
product(g1,b,b,c),
inference(cnf_transformation,[],[f28]) ).
tcf(c_119,plain,
product(g1,b,c,a),
inference(cnf_transformation,[],[f29]) ).
tcf(c_120,plain,
product(g1,c,b,a),
inference(cnf_transformation,[],[f30]) ).
tcf(c_121,plain,
product(g1,c,c,b),
inference(cnf_transformation,[],[f31]) ).
tcf(c_122,plain,
product(g2,f,f,f),
inference(cnf_transformation,[],[f32]) ).
tcf(c_123,plain,
product(g2,f,g,g),
inference(cnf_transformation,[],[f33]) ).
tcf(c_124,plain,
product(g2,g,f,g),
inference(cnf_transformation,[],[f34]) ).
tcf(c_125,plain,
product(g2,f,h,h),
inference(cnf_transformation,[],[f35]) ).
tcf(c_126,plain,
product(g2,h,f,h),
inference(cnf_transformation,[],[f36]) ).
tcf(c_127,plain,
product(g2,g,g,h),
inference(cnf_transformation,[],[f37]) ).
tcf(c_128,plain,
product(g2,g,h,f),
inference(cnf_transformation,[],[f38]) ).
tcf(c_129,plain,
product(g2,h,g,f),
inference(cnf_transformation,[],[f39]) ).
tcf(c_130,plain,
product(g2,h,h,g),
inference(cnf_transformation,[],[f40]) ).
tcf(c_131,plain,
an_isomorphism(a) = f,
inference(cnf_transformation,[],[f42]) ).
tcf(c_132,plain,
an_isomorphism(b) = g,
inference(cnf_transformation,[],[f44]) ).
tcf(c_133,plain,
an_isomorphism(c) = h,
inference(cnf_transformation,[],[f46]) ).
tcf(c_134,plain,
group_member(d1,g1),
inference(cnf_transformation,[],[f47]) ).
tcf(c_135,plain,
group_member(d2,g1),
inference(cnf_transformation,[],[f48]) ).
tcf(c_137,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[],[f50]) ).
tcf(c_138,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_336,definition,
iPr_def_10 = an_isomorphism(d1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_337,definition,
iPr_def_11 = an_isomorphism(d2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_338,definition,
iPr_def_12 = an_isomorphism(d3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_339,negated_conjecture,
~ product(g2,iPr_def_10,iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_138,c_338,c_337,c_336]) ).
tcf(c_732,plain,
! [X0: $i] :
( ( X0 = b )
| ~ product(g1,a,b,X0) ),
inference(superposition,[status(thm)],[c_114,c_102]) ).
tcf(c_736,plain,
! [X0: $i] :
( ( X0 = c )
| ~ product(g1,b,b,X0) ),
inference(superposition,[status(thm)],[c_118,c_102]) ).
tcf(c_737,plain,
! [X0: $i] :
( ( X0 = a )
| ~ product(g1,b,c,X0) ),
inference(superposition,[status(thm)],[c_119,c_102]) ).
tcf(c_738,plain,
! [X0: $i] :
( ( X0 = a )
| ~ product(g1,c,b,X0) ),
inference(superposition,[status(thm)],[c_120,c_102]) ).
tcf(c_739,plain,
! [X0: $i] :
( ( X0 = b )
| ~ product(g1,c,c,X0) ),
inference(superposition,[status(thm)],[c_121,c_102]) ).
tcf(c_747,plain,
! [X0: $i] :
( ( X0 = f )
| ~ product(g2,h,g,X0) ),
inference(superposition,[status(thm)],[c_129,c_102]) ).
tcf(c_748,plain,
! [X0: $i] :
( ( X0 = g )
| ~ product(g2,h,h,X0) ),
inference(superposition,[status(thm)],[c_130,c_102]) ).
tcf(c_749,plain,
! [X0: $i] :
( ( X0 = d3 )
| ~ product(g1,d1,d2,X0) ),
inference(superposition,[status(thm)],[c_137,c_102]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_95,c_102]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(superposition,[status(thm)],[c_96,c_102]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( identity_for(X0) = X2 )
| ~ product(X0,inverse(X0,X1),X1,X2) ),
inference(superposition,[status(thm)],[c_98,c_102]) ).
tcf(c_838,plain,
( ( c = d1 )
| ( b = d1 )
| ( a = d1 ) ),
inference(superposition,[status(thm)],[c_134,c_111]) ).
tcf(c_839,plain,
( ( c = d2 )
| ( b = d2 )
| ( a = d2 ) ),
inference(superposition,[status(thm)],[c_135,c_111]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(superposition,[status(thm)],[c_113,c_103]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(superposition,[status(thm)],[c_114,c_103]) ).
tcf(c_1078,plain,
( ( multiply(g1,b,b) = c )
| ~ group_member(b,g1) ),
inference(superposition,[status(thm)],[c_100,c_736]) ).
tcf(c_1079,plain,
multiply(g1,b,b) = c,
inference(forward_subsumption_resolution,[status(thm)],[c_1078,c_106]) ).
tcf(c_1092,plain,
! [X0: $i] :
( product(g1,a,identity_for(g1),X0)
| ~ product(g1,a,inverse(g1,a),X0) ),
inference(superposition,[status(thm)],[c_99,c_875]) ).
tcf(c_1222,plain,
( ( multiply(g1,b,c) = a )
| ~ group_member(c,g1)
| ~ group_member(b,g1) ),
inference(superposition,[status(thm)],[c_100,c_737]) ).
tcf(c_1223,plain,
multiply(g1,b,c) = a,
inference(forward_subsumption_resolution,[status(thm)],[c_1222,c_107,c_106]) ).
tcf(c_1231,plain,
( ( multiply(g1,c,b) = a )
| ~ group_member(c,g1)
| ~ group_member(b,g1) ),
inference(superposition,[status(thm)],[c_100,c_738]) ).
tcf(c_1232,plain,
multiply(g1,c,b) = a,
inference(forward_subsumption_resolution,[status(thm)],[c_1231,c_107,c_106]) ).
tcf(c_1240,plain,
( ( multiply(g1,c,c) = b )
| ~ group_member(c,g1) ),
inference(superposition,[status(thm)],[c_100,c_739]) ).
tcf(c_1241,plain,
multiply(g1,c,c) = b,
inference(forward_subsumption_resolution,[status(thm)],[c_1240,c_107]) ).
tcf(c_1319,plain,
! [X0: $i] :
( product(g1,a,b,X0)
| ~ product(g1,b,identity_for(g1),X0) ),
inference(superposition,[status(thm)],[c_96,c_876]) ).
tcf(c_1367,plain,
( ( multiply(g2,h,g) = f )
| ~ group_member(h,g2)
| ~ group_member(g,g2) ),
inference(superposition,[status(thm)],[c_100,c_747]) ).
tcf(c_1368,plain,
multiply(g2,h,g) = f,
inference(forward_subsumption_resolution,[status(thm)],[c_1367,c_110,c_109]) ).
tcf(c_1376,plain,
( ( multiply(g2,h,h) = g )
| ~ group_member(h,g2) ),
inference(superposition,[status(thm)],[c_100,c_748]) ).
tcf(c_1377,plain,
multiply(g2,h,h) = g,
inference(forward_subsumption_resolution,[status(thm)],[c_1376,c_110]) ).
tcf(c_1385,plain,
( ( multiply(g1,d1,d2) = d3 )
| ~ group_member(d2,g1)
| ~ group_member(d1,g1) ),
inference(superposition,[status(thm)],[c_100,c_749]) ).
tcf(c_1386,plain,
multiply(g1,d1,d2) = d3,
inference(forward_subsumption_resolution,[status(thm)],[c_1385,c_135,c_134]) ).
tcf(c_1395,plain,
! [X0: $i] : inverse(X0,identity_for(X0)) = identity_for(X0),
inference(superposition,[status(thm)],[c_99,c_750]) ).
tcf(c_1396,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,identity_for(X0),X1) = X1 )
| ~ group_member(X1,X0)
| ~ group_member(identity_for(X0),X0) ),
inference(superposition,[status(thm)],[c_100,c_750]) ).
tcf(c_1397,plain,
! [X0: $i,X1: $i] :
( ( multiply(X1,identity_for(X1),X0) = X0 )
| ~ group_member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1396,c_94]) ).
tcf(c_1412,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1,identity_for(X0)) = X1 )
| ~ group_member(X1,X0)
| ~ group_member(identity_for(X0),X0) ),
inference(superposition,[status(thm)],[c_100,c_751]) ).
tcf(c_1413,plain,
! [X0: $i,X1: $i] :
( ( multiply(X1,X0,identity_for(X1)) = X0 )
| ~ group_member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1412,c_94]) ).
tcf(c_1469,plain,
( ( b = d1 )
| ( a = d1 )
| ( an_isomorphism(c) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_838,c_336]) ).
tcf(c_1475,plain,
( ( h = iPr_def_10 )
| ( b = d1 )
| ( a = d1 ) ),
inference(light_normalisation,[status(thm)],[c_1469,c_133]) ).
tcf(c_1493,plain,
( ( b = d2 )
| ( a = d2 )
| ( multiply(g1,d1,c) = d3 ) ),
inference(superposition,[status(thm)],[c_839,c_1386]) ).
tcf(c_1495,plain,
( ( b = d2 )
| ( a = d2 )
| ( an_isomorphism(c) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_839,c_337]) ).
tcf(c_1612,plain,
( product(g1,a,b,multiply(g1,b,identity_for(g1)))
| ~ group_member(b,g1)
| ~ group_member(identity_for(g1),g1) ),
inference(superposition,[status(thm)],[c_100,c_1319]) ).
tcf(c_1613,plain,
product(g1,a,b,multiply(g1,b,identity_for(g1))),
inference(forward_subsumption_resolution,[status(thm)],[c_1612,c_106,c_94]) ).
tcf(c_1617,plain,
multiply(g1,b,identity_for(g1)) = b,
inference(superposition,[status(thm)],[c_1613,c_732]) ).
tcf(c_1645,plain,
multiply(g1,identity_for(g1),c) = c,
inference(superposition,[status(thm)],[c_107,c_1397]) ).
tcf(c_1650,plain,
multiply(g1,identity_for(g1),d2) = d2,
inference(superposition,[status(thm)],[c_135,c_1397]) ).
tcf(c_1779,plain,
multiply(g1,c,identity_for(g1)) = c,
inference(superposition,[status(thm)],[c_107,c_1413]) ).
tcf(c_1939,plain,
( ( h = iPr_def_10 )
| ( a = d1 )
| ( multiply(g1,b,d2) = d3 ) ),
inference(superposition,[status(thm)],[c_1475,c_1386]) ).
tcf(c_1941,plain,
( ( h = iPr_def_10 )
| ( a = d1 )
| ( an_isomorphism(b) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1475,c_336]) ).
tcf(c_3882,plain,
product(g1,a,identity_for(g1),identity_for(g1)),
inference(superposition,[status(thm)],[c_99,c_1092]) ).
tcf(c_3892,plain,
identity_for(g1) = a,
inference(superposition,[status(thm)],[c_3882,c_751]) ).
tcf(c_3954,plain,
inverse(g1,a) = a,
inference(superposition,[status(thm)],[c_3892,c_1395]) ).
tcf(c_3958,plain,
! [X0: $i] : product(g1,X0,a,X0),
inference(superposition,[status(thm)],[c_3892,c_96]) ).
tcf(c_3981,plain,
inverse(g1,a) = identity_for(g1),
inference(superposition,[status(thm)],[c_3958,c_752]) ).
tcf(c_4425,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_3981,c_3954,c_1941,c_1939,c_1779,c_1650,c_1645,c_1617,c_1495,c_1493,c_1386,c_1377,c_1368,c_1241,c_1232,c_1223,c_1079,c_839,c_838,c_339,c_338,c_337,c_336,c_133,c_132,c_131,c_130,c_129,c_128,c_127,c_126,c_125,c_124,c_123,c_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.40 % Computer : n018.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.11/5.40 % CPULimit : 300
% 0.11/5.40 % WCLimit : 300
% 0.11/5.40 % DateTime : Wed Sep 23 13:19:55 UTC 2026
% 0.11/5.41 % CPUTime :
% 0.11/5.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.47 Running first-order theorem proving
% 0.11/5.47 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.49
% 0.11/5.49 % ======== iProver multi-core TPTP/SMT =========
% 0.11/5.49
% 0.11/5.49 % Detected problem language: tptp
% 0.19/5.51 % Proving...
% 3.60/6.38 % SZS status Started for theBenchmark.p
% 3.60/6.38 % SZS status Unsatisfiable for theBenchmark.p
% 3.60/6.38
% 3.60/6.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.60/6.38
% 3.60/6.38 % ------ iProver source info
% 3.60/6.38
% 3.60/6.38 % git: date: 2026-07-19 20:42:38 +0200
% 3.60/6.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.60/6.38 % git: non_committed_changes: false
% 3.60/6.38
% 3.60/6.38 % ------ Parsing...% successful
% 3.60/6.38
% 3.60/6.38
% 3.60/6.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.60/6.38
% 3.60/6.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.60/6.38
% 3.60/6.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.60/6.38
% 3.60/6.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.60/6.38 % ------ Proving...
% 3.60/6.38 % ------ Problem Properties
% 3.60/6.38
% 3.60/6.38 %
% 3.60/6.38 % clauses 48
% 3.60/6.38 % conjectures 1
% 3.60/6.38 % EPR 34
% 3.60/6.38 % Horn 46
% 3.60/6.38 % unary 40
% 3.60/6.38 % binary 1
% 3.60/6.38 % lits 67
% 3.60/6.38 % lits eq 13
% 3.60/6.38 % fd_pure 0
% 3.60/6.38 % fd_pseudo 0
% 3.60/6.38 % fd_cond 2
% 3.60/6.38 % fd_pseudo_cond 1
% 3.60/6.38 % AC symbols 0
% 3.60/6.38
% 3.60/6.38 % ------ Schedule dynamic 5 is on
% 3.60/6.38
% 3.60/6.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.60/6.38
% 3.60/6.38
% 3.60/6.38 % ------
% 3.60/6.38 % Current options:
% 3.60/6.38 % ------
% 3.60/6.38
% 3.60/6.38
% 3.60/6.38 %
% 3.60/6.38
% 3.60/6.38 % ------ Proving...
% 3.60/6.38 %
% 3.60/6.38
% 3.60/6.38 % SZS status Unsatisfiable for theBenchmark.p
% 3.60/6.38
% 3.60/6.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.60/6.39
%------------------------------------------------------------------------------