%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP203-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 01:31:48 PM UTC 2026
% Result : Unsatisfiable 17.45s 8.28s
% Output : CNFRefutation 17.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 61 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 110 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(left_inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(left_inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',moufang3) ).
fof(f5,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_moufang2) ).
tcf(c_53,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,plain,
! [X0: $i] : multiply(left_inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(X0,X1),X0),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_56,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,multiply(identity,X1))) = multiply(multiply(X0,identity),X1),
inference(superposition,[status(thm)],[c_53,c_55]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),multiply(X0,multiply(left_inverse(X0),X1))) = multiply(multiply(identity,left_inverse(X0)),X1),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_679,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,identity),X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_674,c_53]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),multiply(X0,multiply(left_inverse(X0),X1))) = multiply(left_inverse(X0),X1),
inference(demodulation,[status(thm)],[c_675,c_53]) ).
tcf(c_684,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,multiply(X0,identity))),X2) = multiply(multiply(multiply(X0,X1),X0),X2),
inference(superposition,[status(thm)],[c_55,c_679]) ).
tcf(c_686,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(identity,multiply(X0,X1))) = multiply(multiply(X0,X0),X1),
inference(superposition,[status(thm)],[c_679,c_55]) ).
tcf(c_688,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_686,c_53]) ).
tcf(c_689,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,multiply(X0,identity))),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(demodulation,[status(thm)],[c_684,c_55]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(X0,identity)),multiply(X0,multiply(left_inverse(multiply(X0,identity)),X1))) = multiply(left_inverse(multiply(X0,identity)),X1),
inference(superposition,[status(thm)],[c_679,c_680]) ).
tcf(c_738,plain,
! [X0: $i] : multiply(left_inverse(X0),multiply(X0,identity)) = identity,
inference(superposition,[status(thm)],[c_54,c_680]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(multiply(X0,X1),X0)),multiply(X0,multiply(X1,multiply(X0,identity)))) = identity,
inference(superposition,[status(thm)],[c_55,c_738]) ).
tcf(c_850,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(multiply(X0,multiply(X1,X1)),X0)),multiply(X0,multiply(X1,multiply(X1,multiply(X0,identity))))) = identity,
inference(superposition,[status(thm)],[c_688,c_745]) ).
tcf(c_1125,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_inverse(X0),multiply(X0,X1))) = multiply(multiply(X0,identity),X1),
inference(superposition,[status(thm)],[c_738,c_689]) ).
tcf(c_1165,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_inverse(X0),multiply(X0,X1))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_1125,c_679]) ).
tcf(c_1318,plain,
! [X0: $i] : multiply(left_inverse(X0),multiply(left_inverse(left_inverse(X0)),identity)) = identity,
inference(superposition,[status(thm)],[c_738,c_1165]) ).
tcf(c_5459,plain,
! [X0: $i] : multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),left_inverse(X0))),left_inverse(left_inverse(X0)))),multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),identity))) = identity,
inference(superposition,[status(thm)],[c_1318,c_850]) ).
tcf(c_5492,plain,
! [X0: $i] : multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),left_inverse(X0))),left_inverse(left_inverse(X0)))),identity) = identity,
inference(demodulation,[status(thm)],[c_5459,c_738]) ).
tcf(c_5785,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),left_inverse(X0))),left_inverse(left_inverse(X0)))),X1) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_5492,c_679]) ).
tcf(c_5794,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),left_inverse(X0))),left_inverse(left_inverse(X0)))),X1) = X1,
inference(demodulation,[status(thm)],[c_5785,c_53]) ).
tcf(c_5903,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),left_inverse(X0))),left_inverse(left_inverse(X0)))),multiply(multiply(multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),left_inverse(X0))),left_inverse(left_inverse(X0))),X1)) = X1,
inference(superposition,[status(thm)],[c_5794,c_680]) ).
tcf(c_5979,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),multiply(left_inverse(X0),multiply(left_inverse(left_inverse(X0)),X1)))) = X1,
inference(demodulation,[status(thm)],[c_5903,c_55,c_688,c_5794]) ).
tcf(c_6344,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(left_inverse(X0)),multiply(left_inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_5979,c_680]) ).
tcf(c_6481,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(left_inverse(multiply(X0,identity))),multiply(left_inverse(multiply(X0,identity)),X1)) = multiply(X0,multiply(left_inverse(multiply(X0,identity)),X1)),
inference(superposition,[status(thm)],[c_735,c_6344]) ).
tcf(c_6534,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_inverse(multiply(X0,identity)),X1)) = X1,
inference(demodulation,[status(thm)],[c_6481,c_6344]) ).
tcf(c_8040,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(left_inverse(multiply(X0,identity)),identity)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_6534,c_6534]) ).
tcf(c_8047,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(X0,identity)),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_8040,c_6534]) ).
tcf(c_8056,plain,
! [X0: $i] : multiply(left_inverse(multiply(left_inverse(X0),identity)),identity) = X0,
inference(superposition,[status(thm)],[c_54,c_8047]) ).
tcf(c_8069,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,multiply(identity,X1))) = multiply(multiply(X0,identity),X1),
inference(superposition,[status(thm)],[c_53,c_55]) ).
tcf(c_8083,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,identity),X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_8069,c_53]) ).
tcf(c_8105,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(left_inverse(X0),identity)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_8056,c_8083]) ).
tcf(c_8137,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_8105,c_6534]) ).
tcf(c_8141,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(left_inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_8105,c_8047]) ).
tcf(c_8142,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_8105,c_8056]) ).
tcf(c_8156,plain,
! [X0: $i] : multiply(left_inverse(left_inverse(X0)),identity) = X0,
inference(demodulation,[status(thm)],[c_8056,c_8142]) ).
tcf(c_8167,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,identity))) = multiply(multiply(X0,X1),X0),
inference(superposition,[status(thm)],[c_8142,c_55]) ).
tcf(c_8168,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),X0) = multiply(X0,multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_8167,c_8142]) ).
tcf(c_8171,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,multiply(X1,X0)),X2) = multiply(X0,multiply(X1,multiply(X0,X2))),
inference(demodulation,[status(thm)],[c_55,c_8168]) ).
tcf(c_8174,plain,
! [X0: $i] : left_inverse(left_inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_8156,c_8142]) ).
tcf(c_8291,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_8168,c_8137]) ).
tcf(c_8459,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),multiply(X1,multiply(multiply(left_inverse(X1),X0),X1))) = X1,
inference(superposition,[status(thm)],[c_8141,c_8291]) ).
tcf(c_9231,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(X0,left_inverse(X1))),multiply(X1,multiply(left_inverse(X1),multiply(X0,multiply(left_inverse(X1),X1))))) = X1,
inference(superposition,[status(thm)],[c_8171,c_8459]) ).
tcf(c_9236,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(X0,left_inverse(X1))),X0) = X1,
inference(demodulation,[status(thm)],[c_9231,c_54,c_8141,c_8142]) ).
tcf(c_9320,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(multiply(X0,X1)),X0) = left_inverse(X1),
inference(superposition,[status(thm)],[c_8174,c_9236]) ).
tcf(c_9335,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,left_inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[c_9236,c_8141]) ).
tcf(c_9384,plain,
! [X0: $i,X1: $i] : left_inverse(multiply(left_inverse(X0),left_inverse(X1))) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_9236,c_9335]) ).
tcf(c_9387,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),left_inverse(X1)) = X0,
inference(superposition,[status(thm)],[c_8174,c_9335]) ).
tcf(c_9511,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),left_inverse(multiply(X0,X1))) = left_inverse(multiply(X0,multiply(X1,X0))),
inference(superposition,[status(thm)],[c_8291,c_9320]) ).
tcf(c_9521,plain,
! [X0: $i,X1: $i] : multiply(left_inverse(X0),left_inverse(X1)) = left_inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_9320,c_9387]) ).
tcf(c_9542,plain,
! [X0: $i,X1: $i] : left_inverse(multiply(left_inverse(X0),X1)) = multiply(left_inverse(X1),X0),
inference(superposition,[status(thm)],[c_9320,c_9335]) ).
tcf(c_41228,plain,
! [X0: $i,X1: $i,X2: $i] : left_inverse(multiply(multiply(left_inverse(X0),left_inverse(multiply(X0,X1))),left_inverse(X2))) = multiply(X2,multiply(X0,multiply(X1,X0))),
inference(superposition,[status(thm)],[c_9511,c_9384]) ).
tcf(c_41309,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(X0,X1),X2),X1) = multiply(X0,multiply(X1,multiply(X2,X1))),
inference(demodulation,[status(thm)],[c_41228,c_8171,c_9384,c_9542,c_9521]) ).
tcf(c_41443,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_41309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP203-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n011.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 14:08:03 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running UEQ theorem proving
% 0.16/5.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 17.45/8.28 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 17.45/8.28 % SZS status Started for theBenchmark.p
% 17.45/8.28 % SZS status Unsatisfiable for theBenchmark.p
% 17.45/8.28
% 17.45/8.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.45/8.28
% 17.45/8.28 % ------ iProver source info
% 17.45/8.28
% 17.45/8.28 % git: date: 2026-07-19 20:42:38 +0200
% 17.45/8.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.45/8.28 % git: non_committed_changes: false
% 17.45/8.28
% 17.45/8.28 % ------ Parsing...% successful
% 17.45/8.28
% 17.45/8.28
% 17.45/8.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.45/8.28
% 17.45/8.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 17.45/8.28
% 17.45/8.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.45/8.28
% 17.45/8.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 17.45/8.28 % ------ Proving...
% 17.45/8.28 % ------ Problem Properties
% 17.45/8.28
% 17.45/8.28 %
% 17.45/8.28 % clauses 4
% 17.45/8.28 % conjectures 1
% 17.45/8.28 % EPR 0
% 17.45/8.28 % Horn 4
% 17.45/8.28 % unary 4
% 17.45/8.28 % binary 0
% 17.45/8.28 % lits 4
% 17.45/8.28 % lits eq 4
% 17.45/8.28 % fd_pure 0
% 17.45/8.28 % fd_pseudo 0
% 17.45/8.28 % fd_cond 0
% 17.45/8.28 % fd_pseudo_cond 0
% 17.45/8.28 % AC symbols 0
% 17.45/8.28
% 17.45/8.28 % ------ Input Options Time Limit: Unbounded
% 17.45/8.28
% 17.45/8.28
% 17.45/8.28 % ------
% 17.45/8.28 % Current options:
% 17.45/8.28 % ------
% 17.45/8.28
% 17.45/8.28
% 17.45/8.28 %
% 17.45/8.28
% 17.45/8.28 % ------ Proving...
% 17.45/8.28 %
% 17.45/8.28
% 17.45/8.28 % SZS status Unsatisfiable for theBenchmark.p
% 17.45/8.28
% 17.45/8.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.45/8.28
% 17.45/8.28
%------------------------------------------------------------------------------