%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 01:30:00 PM UTC 2026
% Result : Unsatisfiable 3.55s 1.11s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 56 unt; 3 def)
% Number of atoms : 195 ( 48 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 33 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_inverse) ).
fof(f6,axiom,
! [X2,X0,X1] :
( subgroup_member(X2)
| multiply(X0,X1) != X2
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f8,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f9,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f11,axiom,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f12,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
fof(f13,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f14,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f15,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f16,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
tcf(c_62,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_67,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,X1)) = X1 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_71,negated_conjecture,
subgroup_member(b),
inference(cnf_transformation,[],[f12]) ).
tcf(c_72,negated_conjecture,
multiply(b,inverse(a)) = c,
inference(cnf_transformation,[],[f13]) ).
tcf(c_73,negated_conjecture,
multiply(a,c) = d,
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,negated_conjecture,
~ subgroup_member(d),
inference(cnf_transformation,[],[f15]) ).
tcf(c_149,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_150,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_151,definition,
iPr_def_12 = multiply(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_152,negated_conjecture,
~ subgroup_member(d),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_153,negated_conjecture,
iPr_def_10 = d,
inference(demodulation,[status(thm)],[c_73,c_149]) ).
tcf(c_154,negated_conjecture,
iPr_def_12 = c,
inference(demodulation,[status(thm)],[c_72,c_150,c_151]) ).
tcf(c_155,negated_conjecture,
subgroup_member(b),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_308,plain,
~ subgroup_member(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_152,c_153]) ).
tcf(c_311,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_150,c_65]) ).
tcf(c_318,plain,
multiply(a,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_149,c_154]) ).
tcf(c_320,plain,
multiply(iPr_def_11,a) = identity,
inference(superposition,[status(thm)],[c_150,c_63]) ).
tcf(c_344,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_151,c_66]) ).
tcf(c_345,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_318,c_66]) ).
tcf(c_351,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_345,c_308]) ).
tcf(c_354,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_344,c_155]) ).
tcf(c_364,plain,
~ subgroup_member(a),
inference(global_subsumption_just,[status(thm)],[c_351,c_311,c_354,c_351]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_68,c_64]) ).
tcf(c_383,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_151,c_64]) ).
tcf(c_384,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_12,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_318,c_64]) ).
tcf(c_385,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_320,c_64]) ).
tcf(c_392,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_385,c_62]) ).
tcf(c_419,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,iPr_def_10)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_70,c_308]) ).
tcf(c_422,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(iPr_def_10,element_in_O2(iPr_def_10,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_70,c_308]) ).
tcf(c_469,plain,
multiply(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_318,c_392]) ).
tcf(c_471,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(iPr_def_10,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_384,c_392]) ).
tcf(c_506,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(iPr_def_11,X0)) ),
inference(superposition,[status(thm)],[c_383,c_66]) ).
tcf(c_509,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(multiply(iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_506,c_155]) ).
tcf(c_526,plain,
( subgroup_member(multiply(iPr_def_12,iPr_def_10))
| ~ subgroup_member(iPr_def_12) ),
inference(superposition,[status(thm)],[c_469,c_509]) ).
tcf(c_555,plain,
multiply(a,element_in_O2(a,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_419,c_364]) ).
tcf(c_572,plain,
multiply(iPr_def_10,element_in_O2(iPr_def_10,a)) = a,
inference(superposition,[status(thm)],[c_422,c_364]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_379,c_62]) ).
tcf(c_585,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_68,c_581]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(inverse(X0),X1)) ),
inference(superposition,[status(thm)],[c_581,c_66]) ).
tcf(c_603,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_585,c_67]) ).
tcf(c_644,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_603,c_65]) ).
tcf(c_1016,plain,
multiply(iPr_def_11,iPr_def_10) = element_in_O2(a,iPr_def_10),
inference(superposition,[status(thm)],[c_555,c_392]) ).
tcf(c_1017,plain,
element_in_O2(a,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1016,c_469]) ).
tcf(c_1020,plain,
( subgroup_member(iPr_def_12)
| subgroup_member(iPr_def_10)
| subgroup_member(a) ),
inference(superposition,[status(thm)],[c_1017,c_69]) ).
tcf(c_1021,plain,
subgroup_member(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_1020,c_308,c_364]) ).
tcf(c_1022,plain,
subgroup_member(multiply(iPr_def_12,iPr_def_10)),
inference(backward_subsumption_resolution,[status(thm)],[c_526,c_1021]) ).
tcf(c_1074,plain,
multiply(iPr_def_12,element_in_O2(iPr_def_10,a)) = multiply(iPr_def_11,a),
inference(superposition,[status(thm)],[c_572,c_471]) ).
tcf(c_1082,plain,
multiply(iPr_def_12,element_in_O2(iPr_def_10,a)) = identity,
inference(light_normalisation,[status(thm)],[c_1074,c_320]) ).
tcf(c_1872,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(element_in_O2(iPr_def_10,a),X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1082,c_64]) ).
tcf(c_1888,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(element_in_O2(iPr_def_10,a),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1872,c_62]) ).
tcf(c_1994,plain,
inverse(element_in_O2(iPr_def_10,a)) = multiply(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_68,c_1888]) ).
tcf(c_2083,plain,
inverse(element_in_O2(iPr_def_10,a)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1994,c_67]) ).
tcf(c_2084,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(element_in_O2(iPr_def_10,a))
| ~ subgroup_member(multiply(iPr_def_12,X0)) ),
inference(superposition,[status(thm)],[c_2083,c_592]) ).
tcf(c_2085,plain,
( subgroup_member(element_in_O2(iPr_def_10,a))
| ~ subgroup_member(iPr_def_12) ),
inference(superposition,[status(thm)],[c_2083,c_644]) ).
tcf(c_2091,plain,
subgroup_member(element_in_O2(iPr_def_10,a)),
inference(forward_subsumption_resolution,[status(thm)],[c_2085,c_1021]) ).
tcf(c_2092,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(multiply(iPr_def_12,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2084,c_2091]) ).
tcf(c_2231,plain,
subgroup_member(iPr_def_10),
inference(superposition,[status(thm)],[c_1022,c_2092]) ).
tcf(c_2241,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2231,c_308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.06/0.31 % Computer : n012.cluster.edu
% 0.06/0.31 % Model : x86_64 x86_64
% 0.06/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.31 % Memory : 8046.5625MB
% 0.06/0.31 % OS : Linux 6.8.0-71-generic
% 0.06/0.31 % CPULimit : 300
% 0.06/0.31 % WCLimit : 300
% 0.06/0.31 % DateTime : Wed Sep 23 13:20:55 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.34 Running first-order theorem proving
% 0.09/0.34 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
% 0.09/0.35
% 0.09/0.35 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.35
% 0.09/0.35 % Detected problem language: tptp
% 0.09/0.36 % Proving...
% 3.55/1.11 % SZS status Started for theBenchmark.p
% 3.55/1.11 % SZS status Unsatisfiable for theBenchmark.p
% 3.55/1.11
% 3.55/1.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.55/1.11
% 3.55/1.11 % ------ iProver source info
% 3.55/1.11
% 3.55/1.11 % git: date: 2026-07-19 20:42:38 +0200
% 3.55/1.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.55/1.11 % git: non_committed_changes: false
% 3.55/1.11
% 3.55/1.11 % ------ Parsing...% successful
% 3.55/1.11
% 3.55/1.11
% 3.55/1.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.55/1.11
% 3.55/1.11 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.55/1.11
% 3.55/1.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.55/1.11
% 3.55/1.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.55/1.11 % ------ Proving...
% 3.55/1.11 % ------ Problem Properties
% 3.55/1.11
% 3.55/1.11 %
% 3.55/1.11 % clauses 16
% 3.55/1.11 % conjectures 4
% 3.55/1.11 % EPR 4
% 3.55/1.11 % Horn 14
% 3.55/1.11 % unary 12
% 3.55/1.11 % binary 1
% 3.55/1.11 % lits 23
% 3.55/1.11 % lits eq 11
% 3.55/1.11 % fd_pure 0
% 3.55/1.11 % fd_pseudo 0
% 3.55/1.11 % fd_cond 0
% 3.55/1.11 % fd_pseudo_cond 0
% 3.55/1.11 % AC symbols 0
% 3.55/1.11
% 3.55/1.11 % ------ Schedule dynamic 5 is on
% 3.55/1.11
% 3.55/1.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.55/1.11
% 3.55/1.11
% 3.55/1.11 % ------
% 3.55/1.11 % Current options:
% 3.55/1.11 % ------
% 3.55/1.11
% 3.55/1.11
% 3.55/1.11 %
% 3.55/1.11
% 3.55/1.11 % ------ Proving...
% 3.55/1.11 %
% 3.55/1.11
% 3.55/1.11 % SZS status Unsatisfiable for theBenchmark.p
% 3.55/1.11
% 3.55/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.11
% 3.55/1.11
%------------------------------------------------------------------------------