%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 01:29:56 PM UTC 2026
% Result : Unsatisfiable 3.81s 1.28s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 86 ( 48 unt; 3 def)
% Number of atoms : 159 ( 72 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 28 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 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 : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?; 31 :)
% 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(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(f13,axiom,
group_member(a,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_member_of_group1) ).
fof(f14,axiom,
group_member(b,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_member_of_group1) ).
fof(f17,axiom,
! [X0] :
( X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
fof(f18,plain,
! [X0] :
( b = X0
| a = X0
| ~ group_member(X0,g1) ),
inference(reorient_equations,[],[f17]) ).
fof(f24,axiom,
product(g1,b,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_a) ).
fof(f25,axiom,
product(g2,c,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_c) ).
fof(f26,axiom,
product(g2,c,d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_d_is_d) ).
fof(f27,axiom,
product(g2,d,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_c_is_d) ).
fof(f28,axiom,
product(g2,d,d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_d_is_c) ).
fof(f29,axiom,
an_isomorphism(a) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_c) ).
fof(f30,plain,
c = an_isomorphism(a),
inference(reorient_equations,[],[f29]) ).
fof(f31,axiom,
an_isomorphism(b) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_d) ).
fof(f32,plain,
d = an_isomorphism(b),
inference(reorient_equations,[],[f31]) ).
fof(f33,axiom,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_member_of_group1) ).
fof(f34,axiom,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_member_of_group1) ).
fof(f35,axiom,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_member_of_group1) ).
fof(f36,axiom,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
fof(f37,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_81,plain,
! [X0: $i] : group_member(identity_for(X0),X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : product(X0,identity_for(X0),X1,X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : product(X0,X1,identity_for(X0),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,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_89,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_92,plain,
group_member(a,g1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_93,plain,
group_member(b,g1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_96,plain,
! [X0: $i] :
( ( X0 = b )
| ( X0 = a )
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_101,plain,
product(g1,b,b,a),
inference(cnf_transformation,[],[f24]) ).
tcf(c_102,plain,
product(g2,c,c,c),
inference(cnf_transformation,[],[f25]) ).
tcf(c_103,plain,
product(g2,c,d,d),
inference(cnf_transformation,[],[f26]) ).
tcf(c_104,plain,
product(g2,d,c,d),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,plain,
product(g2,d,d,c),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,plain,
an_isomorphism(a) = c,
inference(cnf_transformation,[],[f30]) ).
tcf(c_107,plain,
an_isomorphism(b) = d,
inference(cnf_transformation,[],[f32]) ).
tcf(c_108,plain,
group_member(d1,g1),
inference(cnf_transformation,[],[f33]) ).
tcf(c_109,plain,
group_member(d2,g1),
inference(cnf_transformation,[],[f34]) ).
tcf(c_110,plain,
group_member(d3,g1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_111,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[],[f36]) ).
tcf(c_112,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_276,definition,
iPr_def_10 = an_isomorphism(d1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_277,definition,
iPr_def_11 = an_isomorphism(d2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_278,definition,
iPr_def_12 = an_isomorphism(d3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_279,negated_conjecture,
~ product(g2,iPr_def_10,iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_112,c_278,c_277,c_276]) ).
tcf(c_588,plain,
( ( b = d1 )
| ( a = d1 ) ),
inference(superposition,[status(thm)],[c_108,c_96]) ).
tcf(c_589,plain,
( ( b = d2 )
| ( a = d2 ) ),
inference(superposition,[status(thm)],[c_109,c_96]) ).
tcf(c_590,plain,
( ( b = d3 )
| ( a = d3 ) ),
inference(superposition,[status(thm)],[c_110,c_96]) ).
tcf(c_591,plain,
( ( identity_for(g1) = b )
| ( identity_for(g1) = a ) ),
inference(superposition,[status(thm)],[c_81,c_96]) ).
tcf(c_609,plain,
( ( a = d1 )
| ( an_isomorphism(b) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_588,c_276]) ).
tcf(c_614,plain,
( ( d = iPr_def_10 )
| ( a = d1 ) ),
inference(light_normalisation,[status(thm)],[c_609,c_107]) ).
tcf(c_621,plain,
( ( a = d2 )
| ( an_isomorphism(b) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_589,c_277]) ).
tcf(c_626,plain,
( ( d = iPr_def_11 )
| ( a = d2 ) ),
inference(light_normalisation,[status(thm)],[c_621,c_107]) ).
tcf(c_633,plain,
( ( a = d3 )
| ( an_isomorphism(b) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_590,c_278]) ).
tcf(c_638,plain,
( ( d = iPr_def_12 )
| ( a = d3 ) ),
inference(light_normalisation,[status(thm)],[c_633,c_107]) ).
tcf(c_662,plain,
( product(g1,d1,a,d3)
| ( d = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_626,c_111]) ).
tcf(c_675,plain,
( ( d = iPr_def_12 )
| ( an_isomorphism(a) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_638,c_278]) ).
tcf(c_680,plain,
( ( d = iPr_def_12 )
| ( c = iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_675,c_106]) ).
tcf(c_740,plain,
( product(g2,c,iPr_def_12,iPr_def_12)
| ( c = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_680,c_103]) ).
tcf(c_831,plain,
! [X0: $i] :
( ( X0 = a )
| ~ product(g1,b,b,X0) ),
inference(superposition,[status(thm)],[c_101,c_89]) ).
tcf(c_836,plain,
! [X0: $i] :
( ( X0 = d3 )
| ~ product(g1,d1,d2,X0) ),
inference(superposition,[status(thm)],[c_111,c_89]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(superposition,[status(thm)],[c_82,c_89]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(superposition,[status(thm)],[c_83,c_89]) ).
tcf(c_1742,plain,
( ( multiply(g1,b,b) = a )
| ~ group_member(b,g1) ),
inference(superposition,[status(thm)],[c_87,c_831]) ).
tcf(c_1743,plain,
multiply(g1,b,b) = a,
inference(forward_subsumption_resolution,[status(thm)],[c_1742,c_93]) ).
tcf(c_2041,plain,
( ( multiply(g1,d1,d2) = d3 )
| ~ group_member(d2,g1)
| ~ group_member(d1,g1) ),
inference(superposition,[status(thm)],[c_87,c_836]) ).
tcf(c_2048,plain,
multiply(g1,d1,d2) = d3,
inference(forward_subsumption_resolution,[status(thm)],[c_2041,c_109,c_108]) ).
tcf(c_2071,plain,
( ( a = d1 )
| ( multiply(g1,b,d2) = d3 ) ),
inference(superposition,[status(thm)],[c_588,c_2048]) ).
tcf(c_2318,plain,
! [X0: $i] : inverse(X0,identity_for(X0)) = identity_for(X0),
inference(superposition,[status(thm)],[c_86,c_837]) ).
tcf(c_2334,plain,
( ( identity_for(g1) = a )
| ( inverse(g1,b) = b ) ),
inference(superposition,[status(thm)],[c_591,c_2318]) ).
tcf(c_2890,plain,
( ( a = d2 )
| ( a = d1 )
| ( multiply(g1,b,b) = d3 ) ),
inference(superposition,[status(thm)],[c_589,c_2071]) ).
tcf(c_2934,plain,
( product(g1,b,b,identity_for(g1))
| ( identity_for(g1) = a ) ),
inference(superposition,[status(thm)],[c_2334,c_86]) ).
tcf(c_3029,plain,
identity_for(g1) = a,
inference(forward_subsumption_resolution,[status(thm)],[c_2934,c_831]) ).
tcf(c_3032,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ product(g1,X0,a,X1) ),
inference(superposition,[status(thm)],[c_3029,c_838]) ).
tcf(c_3034,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ product(g1,a,X0,X1) ),
inference(superposition,[status(thm)],[c_3029,c_837]) ).
tcf(c_3138,plain,
( ( d1 = d3 )
| ( d = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_662,c_3032]) ).
tcf(c_3159,plain,
( ( d = iPr_def_12 )
| ( d = iPr_def_11 )
| ( a = d1 ) ),
inference(superposition,[status(thm)],[c_3138,c_638]) ).
tcf(c_3605,plain,
! [X0: $i] :
( ( multiply(g1,a,X0) = X0 )
| ~ group_member(a,g1)
| ~ group_member(X0,g1) ),
inference(superposition,[status(thm)],[c_87,c_3034]) ).
tcf(c_3612,plain,
! [X0: $i] :
( ( multiply(g1,a,X0) = X0 )
| ~ group_member(X0,g1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3605,c_92]) ).
tcf(c_4126,plain,
multiply(g1,a,d2) = d2,
inference(superposition,[status(thm)],[c_109,c_3612]) ).
tcf(c_4672,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_4126,c_3159,c_2890,c_2048,c_1743,c_740,c_680,c_626,c_614,c_279,c_278,c_277,c_276,c_106,c_105,c_104,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:17:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 3.81/1.28 % SZS status Started for theBenchmark.p
% 3.81/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.81/1.28
% 3.81/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.81/1.28
% 3.81/1.28 % ------ iProver source info
% 3.81/1.28
% 3.81/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.81/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.81/1.28 % git: non_committed_changes: false
% 3.81/1.28
% 3.81/1.28 % ------ Parsing...% successful
% 3.81/1.28
% 3.81/1.28
% 3.81/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.81/1.28
% 3.81/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.81/1.28
% 3.81/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.81/1.28
% 3.81/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.81/1.28 % ------ Proving...
% 3.81/1.28 % ------ Problem Properties
% 3.81/1.28
% 3.81/1.28 %
% 3.81/1.28 % clauses 35
% 3.81/1.28 % conjectures 1
% 3.81/1.28 % EPR 22
% 3.81/1.28 % Horn 33
% 3.81/1.28 % unary 27
% 3.81/1.28 % binary 1
% 3.81/1.28 % lits 52
% 3.81/1.28 % lits eq 10
% 3.81/1.28 % fd_pure 0
% 3.81/1.28 % fd_pseudo 0
% 3.81/1.28 % fd_cond 2
% 3.81/1.28 % fd_pseudo_cond 1
% 3.81/1.28 % AC symbols 0
% 3.81/1.28
% 3.81/1.28 % ------ Schedule dynamic 5 is on
% 3.81/1.28
% 3.81/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.81/1.28
% 3.81/1.28
% 3.81/1.28 % ------
% 3.81/1.28 % Current options:
% 3.81/1.28 % ------
% 3.81/1.28
% 3.81/1.28
% 3.81/1.28 %
% 3.81/1.28
% 3.81/1.28 % ------ Proving...
% 3.81/1.28 %
% 3.81/1.28
% 3.81/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.81/1.28
% 3.81/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.81/1.28
% 3.81/1.28
%------------------------------------------------------------------------------