%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 01:30:55 PM UTC 2026
% Result : Unsatisfiable 2.50s 6.21s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 41 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 36 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(X2,X1)))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
tcf(c_52,negated_conjecture,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(X2,X1)))))) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(double_divide(X0,inverse(double_divide(X1,inverse(double_divide(X2,X3))))),inverse(double_divide(X0,X2)))) = double_divide(X1,X3),
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(double_divide(double_divide(X0,X1),inverse(double_divide(X2,X1))),X2)) = X0,
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,X2)))) = double_divide(double_divide(X2,X3),inverse(double_divide(X1,X3))),
inference(superposition,[status(thm)],[c_115,c_53]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(inverse(double_divide(X0,X1)),X2),inverse(double_divide(X1,X2))) = X0,
inference(superposition,[status(thm)],[c_121,c_53]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,X2)))),X1)) = X2,
inference(superposition,[status(thm)],[c_121,c_115]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,X1),inverse(double_divide(inverse(double_divide(X2,inverse(double_divide(X0,X3)))),X1))) = double_divide(X2,X3),
inference(superposition,[status(thm)],[c_53,c_202]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(double_divide(double_divide(inverse(double_divide(X0,X1)),X2),X2),inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_202,c_53]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),X2)),X1)))) = X2,
inference(superposition,[status(thm)],[c_115,c_221]) ).
tcf(c_545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(inverse(double_divide(double_divide(double_divide(X0,X1),X2),X3)),X2)) = inverse(double_divide(X0,inverse(double_divide(X3,X1)))),
inference(superposition,[status(thm)],[c_53,c_221]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(double_divide(X0,inverse(double_divide(X1,X2))),X1)),X2) = X0,
inference(superposition,[status(thm)],[c_113,c_115]) ).
tcf(c_1686,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(double_divide(double_divide(X0,X1),X1),X2)) = inverse(double_divide(X0,X2)),
inference(superposition,[status(thm)],[c_338,c_540]) ).
tcf(c_1725,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),inverse(X0))) = X1,
inference(demodulation,[status(thm)],[c_359,c_1686]) ).
tcf(c_1805,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(double_divide(X1,X2)))) = inverse(double_divide(X1,inverse(double_divide(X0,X2)))),
inference(superposition,[status(thm)],[c_53,c_1725]) ).
tcf(c_1811,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(double_divide(X0,X1),X2)),X1)) = inverse(double_divide(X2,inverse(X0))),
inference(superposition,[status(thm)],[c_540,c_1725]) ).
tcf(c_1844,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(b2,inverse(double_divide(a2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_1805]) ).
tcf(c_1850,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(double_divide(X1,inverse(X0))))) = X1,
inference(demodulation,[status(thm)],[c_540,c_1811]) ).
tcf(c_1851,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1844,c_1850]) ).
tcf(c_2081,plain,
! [X0: $i,X1: $i] : inverse(double_divide(double_divide(X0,inverse(X1)),X0)) = X1,
inference(superposition,[status(thm)],[c_1850,c_1850]) ).
tcf(c_2213,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(b3,inverse(double_divide(c3,a3)))) ) ),
inference(demodulation,[status(thm)],[c_1851,c_1805]) ).
tcf(c_2218,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_202,c_2081]) ).
tcf(c_2230,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),inverse(double_divide(X2,X1))) = double_divide(X2,inverse(X0)),
inference(superposition,[status(thm)],[c_2081,c_202]) ).
tcf(c_2241,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_2081,c_650]) ).
tcf(c_2242,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),inverse(X1)) = inverse(double_divide(X0,X1)),
inference(superposition,[status(thm)],[c_2081,c_1850]) ).
tcf(c_2247,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(inverse(double_divide(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[c_202,c_2230]) ).
tcf(c_2381,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,X1)),X2) = double_divide(X0,inverse(double_divide(X1,X2))),
inference(superposition,[status(thm)],[c_2241,c_650]) ).
tcf(c_2383,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(b3,inverse(double_divide(c3,a3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) ) ),
inference(demodulation,[status(thm)],[c_2213,c_2381]) ).
tcf(c_2384,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ) ),
inference(ground_joinability,[status(thm)],[c_2383,c_1805]) ).
tcf(c_2392,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_2247,c_2218]) ).
tcf(c_2393,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_2241,c_2392]) ).
tcf(c_2395,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_2392,c_2241]) ).
tcf(c_2398,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ) ),
inference(demodulation,[status(thm)],[c_2384,c_2393]) ).
tcf(c_2399,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(equality_resolution_simp,[status(thm)],[c_2398]) ).
tcf(c_2638,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),X1)) = double_divide(X0,inverse(X1)),
inference(superposition,[status(thm)],[c_2218,c_2242]) ).
tcf(c_2641,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(X1))) = double_divide(inverse(X0),X1),
inference(superposition,[status(thm)],[c_2218,c_2242]) ).
tcf(c_2651,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(double_divide(X1,X2)))) = double_divide(inverse(X1),double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_1805,c_2641]) ).
tcf(c_2652,plain,
inverse(double_divide(b1,inverse(b1))) != double_divide(inverse(a1),a1),
inference(demodulation,[status(thm)],[c_2399,c_2641]) ).
tcf(c_2661,plain,
double_divide(a1,inverse(a1)) != double_divide(b1,inverse(b1)),
inference(demodulation,[status(thm)],[c_2652,c_2393,c_2641]) ).
tcf(c_2673,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),double_divide(X1,inverse(X2))) = inverse(double_divide(X0,double_divide(inverse(X1),X2))),
inference(superposition,[status(thm)],[c_2638,c_2242]) ).
tcf(c_2918,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),double_divide(X1,X2)) = double_divide(inverse(X1),double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_545,c_1811,c_2651]) ).
tcf(c_2960,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),double_divide(X1,inverse(X1))) = X0,
inference(superposition,[status(thm)],[c_2918,c_2392]) ).
tcf(c_3014,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(X1,inverse(X1)))) = X0,
inference(demodulation,[status(thm)],[c_2960,c_2393,c_2673]) ).
tcf(c_3029,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,inverse(X1))) = inverse(X0),
inference(superposition,[status(thm)],[c_3014,c_2218]) ).
tcf(c_3167,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(X0)) = double_divide(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_3029,c_2395]) ).
tcf(c_3179,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2661,c_3167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n008.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 13:33:34 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 2.50/6.21 % SZS status Started for theBenchmark.p
% 2.50/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 2.50/6.21
% 2.50/6.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.50/6.21
% 2.50/6.21 % ------ iProver source info
% 2.50/6.21
% 2.50/6.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.50/6.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.50/6.21 % git: non_committed_changes: false
% 2.50/6.21
% 2.50/6.21 % ------ Parsing...% successful
% 2.50/6.21
% 2.50/6.21
% 2.50/6.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.50/6.21
% 2.50/6.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.50/6.21
% 2.50/6.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.50/6.21
% 2.50/6.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.50/6.21 % ------ Proving...
% 2.50/6.21 % ------ Problem Properties
% 2.50/6.21
% 2.50/6.21 %
% 2.50/6.21 % clauses 2
% 2.50/6.21 % conjectures 1
% 2.50/6.21 % EPR 0
% 2.50/6.21 % Horn 2
% 2.50/6.21 % unary 1
% 2.50/6.21 % binary 0
% 2.50/6.21 % lits 5
% 2.50/6.21 % lits eq 5
% 2.50/6.21 % fd_pure 0
% 2.50/6.21 % fd_pseudo 0
% 2.50/6.21 % fd_cond 0
% 2.50/6.21 % fd_pseudo_cond 0
% 2.50/6.21 % AC symbols 0
% 2.50/6.21
% 2.50/6.21 % ------ Schedule dynamic 5 is on
% 2.50/6.21
% 2.50/6.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.50/6.21
% 2.50/6.21
% 2.50/6.21 % ------
% 2.50/6.21 % Current options:
% 2.50/6.21 % ------
% 2.50/6.21
% 2.50/6.21
% 2.50/6.21 %
% 2.50/6.21
% 2.50/6.21 % ------ Proving...
% 2.50/6.21 %
% 2.50/6.21
% 2.50/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 2.50/6.21
% 2.50/6.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.50/6.21
% 2.50/6.21
%------------------------------------------------------------------------------