%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN558-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Tue Sep 29 01:48:06 PM UTC 2026
% Result : Unsatisfiable 3.35s 0.70s
% Output : Proof 3.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN558-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 16:24:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.35/0.70 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 3.35/0.70
% 3.35/0.70 % SZS status Unsatisfiable
% 3.35/0.70
% 3.62/0.75 % SZS output start Proof
% 3.62/0.75 Axiom 1 (p2_1): p2(X, X) = true.
% 3.62/0.75 Axiom 2 (p4_2): p4(X, X) = true.
% 3.62/0.75 Axiom 3 (p6_3): p6(c7, f3(X)) = true.
% 3.62/0.75 Axiom 4 (p5_6): p5(c7, X, f3(X)) = true.
% 3.62/0.75 Axiom 5 (p5_4): p5(c7, c10, c9) = true.
% 3.62/0.75 Axiom 6 (p5_5): p5(c7, c10, c8) = true.
% 3.62/0.75 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.62/0.75 Axiom 8 (p2_9): ifeq(p2(X, Y), true, ifeq(p2(X, Z), true, p2(Z, Y), true), true) = true.
% 3.62/0.75 Axiom 9 (p5_11): ifeq(p5(X, Y, Z), true, ifeq(p5(X, W, Y), true, p5(X, W, Z), true), true) = true.
% 3.62/0.75 Axiom 10 (p5_14): ifeq(p5(X, Y, Z), true, ifeq(p4(X, W), true, ifeq(p2(Z, V), true, ifeq(p2(Y, U), true, p5(W, U, V), true), true), true), true) = true.
% 3.62/0.75 Axiom 11 (p2_13): ifeq(p5(c7, X, Y), true, ifeq(p5(c7, X, Z), true, ifeq(p6(c7, Y), true, ifeq(p6(c7, Z), true, p2(Z, Y), true), true), true), true) = true.
% 3.62/0.75
% 3.62/0.75 Goal 1 (not_p5_8): tuple(p5(c7, c9, X), p5(c7, c8, X)) = tuple(true, true).
% 3.62/0.76 The goal is true when:
% 3.62/0.76 X = f3(f3(c10))
% 3.62/0.76
% 3.62/0.76 Proof:
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), p5(c7, c8, f3(f3(c10))))
% 3.62/0.76 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(true, true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 10 (p5_14) R->L }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p4(c7, c7), true, ifeq(p2(f3(f3(c10)), f3(f3(c10))), true, ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true), true), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 1 (p2_1) }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p4(c7, c7), true, ifeq(true, true, ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true), true), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p4(c7, c7), true, ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 2 (p4_2) }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(true, true, ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 4 (p5_6) }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(true, true, ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(p2(f3(c10), f3(c8)), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(true, true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.76 = { by axiom 11 (p2_13) R->L }
% 3.62/0.76 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c10)), true, ifeq(p5(c7, c10, f3(c8)), true, ifeq(p6(c7, f3(c10)), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 4 (p5_6) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p5(c7, c10, f3(c8)), true, ifeq(p6(c7, f3(c10)), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c8)), true, ifeq(p6(c7, f3(c10)), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 3 (p6_3) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c8)), true, ifeq(true, true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c8)), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p5(c7, c10, f3(c8)), true), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 4 (p5_6) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(ifeq(p5(c7, c8, f3(c8)), true, p5(c7, c10, f3(c8)), true), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(ifeq(p5(c7, c8, f3(c8)), true, ifeq(true, true, p5(c7, c10, f3(c8)), true), true), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 6 (p5_5) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(ifeq(p5(c7, c8, f3(c8)), true, ifeq(p5(c7, c10, c8), true, p5(c7, c10, f3(c8)), true), true), true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 9 (p5_11) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(p6(c7, f3(c8)), true, p2(f3(c8), f3(c10)), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 3 (p6_3) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c8), f3(c10)), true), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(p2(f3(c8), f3(c10)), true, p2(f3(c10), f3(c8)), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c8), f3(c10)), true, p2(f3(c10), f3(c8)), true), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 1 (p2_1) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(ifeq(p2(f3(c8), f3(c8)), true, ifeq(p2(f3(c8), f3(c10)), true, p2(f3(c10), f3(c8)), true), true), true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 8 (p2_9) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(ifeq(true, true, p5(c7, f3(c8), f3(f3(c10))), true), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(p5(c7, f3(c8), f3(f3(c10))), true, p5(c7, c8, f3(f3(c10))), true))
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(p5(c7, f3(c8), f3(f3(c10))), true, ifeq(true, true, p5(c7, c8, f3(f3(c10))), true), true))
% 3.62/0.77 = { by axiom 4 (p5_6) R->L }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), ifeq(p5(c7, f3(c8), f3(f3(c10))), true, ifeq(p5(c7, c8, f3(c8)), true, p5(c7, c8, f3(f3(c10))), true), true))
% 3.62/0.77 = { by axiom 9 (p5_11) }
% 3.62/0.77 tuple(p5(c7, c9, f3(f3(c10))), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.77 tuple(ifeq(true, true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 10 (p5_14) R->L }
% 3.62/0.77 tuple(ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p4(c7, c7), true, ifeq(p2(f3(f3(c10)), f3(f3(c10))), true, ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true), true), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 1 (p2_1) }
% 3.62/0.77 tuple(ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p4(c7, c7), true, ifeq(true, true, ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true), true), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p4(c7, c7), true, ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 2 (p4_2) }
% 3.62/0.77 tuple(ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(true, true, ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(ifeq(ifeq(p5(c7, f3(c10), f3(f3(c10))), true, ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 4 (p5_6) }
% 3.62/0.77 tuple(ifeq(ifeq(true, true, ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(ifeq(ifeq(p2(f3(c10), f3(c9)), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.77 tuple(ifeq(ifeq(ifeq(true, true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 11 (p2_13) R->L }
% 3.62/0.77 tuple(ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c10)), true, ifeq(p5(c7, c10, f3(c9)), true, ifeq(p6(c7, f3(c10)), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 4 (p5_6) }
% 3.62/0.77 tuple(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p5(c7, c10, f3(c9)), true, ifeq(p6(c7, f3(c10)), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.77 tuple(ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c9)), true, ifeq(p6(c7, f3(c10)), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 3 (p6_3) }
% 3.62/0.77 tuple(ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c9)), true, ifeq(true, true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.77 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(p5(c7, c10, f3(c9)), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p5(c7, c10, f3(c9)), true), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 4 (p5_6) R->L }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p5(c7, c9, f3(c9)), true, p5(c7, c10, f3(c9)), true), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p5(c7, c9, f3(c9)), true, ifeq(true, true, p5(c7, c10, f3(c9)), true), true), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 5 (p5_4) R->L }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(p5(c7, c9, f3(c9)), true, ifeq(p5(c7, c10, c9), true, p5(c7, c10, f3(c9)), true), true), true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 9 (p5_11) }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(p6(c7, f3(c9)), true, p2(f3(c9), f3(c10)), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 3 (p6_3) }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(ifeq(true, true, p2(f3(c9), f3(c10)), true), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(p2(f3(c9), f3(c10)), true, p2(f3(c10), f3(c9)), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(true, true, ifeq(p2(f3(c9), f3(c10)), true, p2(f3(c10), f3(c9)), true), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 1 (p2_1) R->L }
% 3.62/0.78 tuple(ifeq(ifeq(ifeq(p2(f3(c9), f3(c9)), true, ifeq(p2(f3(c9), f3(c10)), true, p2(f3(c10), f3(c9)), true), true), true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 8 (p2_9) }
% 3.62/0.78 tuple(ifeq(ifeq(true, true, p5(c7, f3(c9), f3(f3(c10))), true), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) }
% 3.62/0.78 tuple(ifeq(p5(c7, f3(c9), f3(f3(c10))), true, p5(c7, c9, f3(f3(c10))), true), true)
% 3.62/0.78 = { by axiom 7 (ifeq_axiom) R->L }
% 3.62/0.78 tuple(ifeq(p5(c7, f3(c9), f3(f3(c10))), true, ifeq(true, true, p5(c7, c9, f3(f3(c10))), true), true), true)
% 3.62/0.78 = { by axiom 4 (p5_6) R->L }
% 3.62/0.78 tuple(ifeq(p5(c7, f3(c9), f3(f3(c10))), true, ifeq(p5(c7, c9, f3(c9)), true, p5(c7, c9, f3(f3(c10))), true), true), true)
% 3.62/0.78 = { by axiom 9 (p5_11) }
% 3.62/0.78 tuple(true, true)
% 3.62/0.78 % SZS output end Proof
% 3.62/0.78
% 3.62/0.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------