%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP039-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 4.06s 1.08s
% Output : CNFRefutation 4.06s
% 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/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-1.ax',closure_of_multiply) ).
fof(f7,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f8,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f9,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f8]) ).
fof(f11,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f12,axiom,
! [X0,X1] :
( multiply(X0,element_in_O2(X0,X1)) = X1
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_O2) ).
fof(f13,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_in_O2) ).
fof(f14,negated_conjecture,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f15,negated_conjecture,
multiply(a,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f16,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f17,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(equality_resolution,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,plain,
! [X0: $i] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,X1)) = X1 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,negated_conjecture,
subgroup_member(b),
inference(cnf_transformation,[],[f13]) ).
tcf(c_74,negated_conjecture,
multiply(b,inverse(a)) = c,
inference(cnf_transformation,[],[f14]) ).
tcf(c_75,negated_conjecture,
multiply(a,c) = d,
inference(cnf_transformation,[],[f15]) ).
tcf(c_76,negated_conjecture,
~ subgroup_member(d),
inference(cnf_transformation,[],[f16]) ).
tcf(c_151,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_152,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_153,definition,
iPr_def_12 = multiply(b,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_154,negated_conjecture,
~ subgroup_member(d),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_155,negated_conjecture,
iPr_def_10 = d,
inference(demodulation,[status(thm)],[c_75,c_151]) ).
tcf(c_156,negated_conjecture,
iPr_def_12 = c,
inference(demodulation,[status(thm)],[c_74,c_152,c_153]) ).
tcf(c_157,negated_conjecture,
subgroup_member(b),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_314,plain,
~ subgroup_member(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_154,c_155]) ).
tcf(c_317,plain,
( subgroup_member(iPr_def_11)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_152,c_66]) ).
tcf(c_320,plain,
multiply(a,iPr_def_12) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_151,c_156]) ).
tcf(c_322,plain,
multiply(iPr_def_11,a) = identity,
inference(superposition,[status(thm)],[c_152,c_64]) ).
tcf(c_350,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11)
| ~ subgroup_member(b) ),
inference(superposition,[status(thm)],[c_153,c_67]) ).
tcf(c_351,plain,
( subgroup_member(iPr_def_10)
| ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(superposition,[status(thm)],[c_320,c_67]) ).
tcf(c_354,plain,
( ~ subgroup_member(iPr_def_12)
| ~ subgroup_member(a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_351,c_314]) ).
tcf(c_357,plain,
( subgroup_member(iPr_def_12)
| ~ subgroup_member(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_350,c_157]) ).
tcf(c_364,plain,
~ subgroup_member(a),
inference(global_subsumption_just,[status(thm)],[c_354,c_317,c_357,c_354]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_69,c_65]) ).
tcf(c_373,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_153,c_65]) ).
tcf(c_374,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_12,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_320,c_65]) ).
tcf(c_375,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_322,c_65]) ).
tcf(c_382,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_375,c_63]) ).
tcf(c_412,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(X0,element_in_O2(X0,iPr_def_10)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_72,c_314]) ).
tcf(c_415,plain,
! [X0: $i] :
( subgroup_member(X0)
| ( multiply(iPr_def_10,element_in_O2(iPr_def_10,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_72,c_314]) ).
tcf(c_462,plain,
multiply(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_320,c_382]) ).
tcf(c_464,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(iPr_def_10,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_374,c_382]) ).
tcf(c_480,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_373,c_67]) ).
tcf(c_483,plain,
! [X0: $i] :
( subgroup_member(multiply(iPr_def_12,X0))
| ~ subgroup_member(multiply(iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_480,c_157]) ).
tcf(c_520,plain,
( subgroup_member(multiply(iPr_def_12,iPr_def_10))
| ~ subgroup_member(iPr_def_12) ),
inference(superposition,[status(thm)],[c_462,c_483]) ).
tcf(c_545,plain,
multiply(a,element_in_O2(a,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_412,c_364]) ).
tcf(c_562,plain,
multiply(iPr_def_10,element_in_O2(iPr_def_10,a)) = a,
inference(superposition,[status(thm)],[c_415,c_364]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_369,c_63]) ).
tcf(c_586,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_69,c_582]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(inverse(X0),X1)) ),
inference(superposition,[status(thm)],[c_582,c_67]) ).
tcf(c_605,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_586,c_68]) ).
tcf(c_637,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[status(thm)],[c_605,c_66]) ).
tcf(c_945,plain,
multiply(iPr_def_11,iPr_def_10) = element_in_O2(a,iPr_def_10),
inference(superposition,[status(thm)],[c_545,c_382]) ).
tcf(c_946,plain,
element_in_O2(a,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_945,c_462]) ).
tcf(c_1007,plain,
( subgroup_member(iPr_def_12)
| subgroup_member(iPr_def_10)
| subgroup_member(a) ),
inference(superposition,[status(thm)],[c_946,c_71]) ).
tcf(c_1008,plain,
subgroup_member(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_1007,c_314,c_364]) ).
tcf(c_1009,plain,
subgroup_member(multiply(iPr_def_12,iPr_def_10)),
inference(backward_subsumption_resolution,[status(thm)],[c_520,c_1008]) ).
tcf(c_1038,plain,
multiply(iPr_def_12,element_in_O2(iPr_def_10,a)) = multiply(iPr_def_11,a),
inference(superposition,[status(thm)],[c_562,c_464]) ).
tcf(c_1046,plain,
multiply(iPr_def_12,element_in_O2(iPr_def_10,a)) = identity,
inference(light_normalisation,[status(thm)],[c_1038,c_322]) ).
tcf(c_1912,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(element_in_O2(iPr_def_10,a),X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1046,c_65]) ).
tcf(c_1930,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(element_in_O2(iPr_def_10,a),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1912,c_63]) ).
tcf(c_2187,plain,
inverse(element_in_O2(iPr_def_10,a)) = multiply(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_69,c_1930]) ).
tcf(c_2300,plain,
inverse(element_in_O2(iPr_def_10,a)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2187,c_68]) ).
tcf(c_2301,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_2300,c_593]) ).
tcf(c_2302,plain,
( subgroup_member(element_in_O2(iPr_def_10,a))
| ~ subgroup_member(iPr_def_12) ),
inference(superposition,[status(thm)],[c_2300,c_637]) ).
tcf(c_2308,plain,
subgroup_member(element_in_O2(iPr_def_10,a)),
inference(forward_subsumption_resolution,[status(thm)],[c_2302,c_1008]) ).
tcf(c_2309,plain,
! [X0: $i] :
( subgroup_member(X0)
| ~ subgroup_member(multiply(iPr_def_12,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2301,c_2308]) ).
tcf(c_2501,plain,
subgroup_member(iPr_def_10),
inference(superposition,[status(thm)],[c_1009,c_2309]) ).
tcf(c_2511,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2501,c_314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP039-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Wed Sep 23 13:21:36 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.29 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.31 Running first-order theorem proving
% 0.04/0.31 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.32
% 0.04/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.32
% 0.04/0.32 % Detected problem language: tptp
% 0.04/0.33 % Proving...
% 4.06/1.08 % SZS status Started for theBenchmark.p
% 4.06/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 4.06/1.08
% 4.06/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.06/1.08
% 4.06/1.08 % ------ iProver source info
% 4.06/1.08
% 4.06/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 4.06/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.06/1.08 % git: non_committed_changes: false
% 4.06/1.08
% 4.06/1.08 % ------ Parsing...% successful
% 4.06/1.08
% 4.06/1.08
% 4.06/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.06/1.08
% 4.06/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.06/1.08
% 4.06/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.06/1.08
% 4.06/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.06/1.08 % ------ Proving...
% 4.06/1.08 % ------ Problem Properties
% 4.06/1.08
% 4.06/1.08 %
% 4.06/1.08 % clauses 17
% 4.06/1.08 % conjectures 4
% 4.06/1.08 % EPR 5
% 4.06/1.08 % Horn 15
% 4.06/1.08 % unary 13
% 4.06/1.08 % binary 1
% 4.06/1.08 % lits 24
% 4.06/1.08 % lits eq 11
% 4.06/1.08 % fd_pure 0
% 4.06/1.08 % fd_pseudo 0
% 4.06/1.08 % fd_cond 0
% 4.06/1.08 % fd_pseudo_cond 0
% 4.06/1.08 % AC symbols 0
% 4.06/1.08
% 4.06/1.08 % ------ Schedule dynamic 5 is on
% 4.06/1.08
% 4.06/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.06/1.08
% 4.06/1.08
% 4.06/1.08 % ------
% 4.06/1.08 % Current options:
% 4.06/1.08 % ------
% 4.06/1.08
% 4.06/1.08
% 4.06/1.08 %
% 4.06/1.08
% 4.06/1.08 % ------ Proving...
% 4.06/1.08 %
% 4.06/1.08
% 4.06/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 4.06/1.08
% 4.06/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.06/1.09
% 4.06/1.09
%------------------------------------------------------------------------------